Putting (y=7x-20) in (x+3y=12) gives (22x=72), so \(x=\frac{36}{11}\) and \(y=\frac{32}{11}\). Fractional coordinates can also be correct graphical solutions.
Step 2
Why this answer is correct
The correct answer is B. (\left\(\frac{36}{11},\frac{32}{11}\right\)). Putting (y=7x-20) in (x+3y=12) gives (22x=72), so \(x=\frac{36}{11}\) and \(y=\frac{32}{11}\). Fractional coordinates can also be correct graphical solutions.
Step 3
Exam Tip
(y=7x-20) को (x+3y=12) में रखने पर (22x=72), इसलिए \(x=\frac{36}{11}\) और \(y=\frac{32}{11}\)। भिन्न निर्देशांक भी सही ग्राफीय समाधान हो सकते हैं।
Substituting (\left\(\frac{5}{2},-\frac{3}{2}\right\)) makes both \(2x+y=\frac{7}{2}\) and \(x-2y=\frac{11}{2}\) true. Check the intersection point in both equations.
Step 2
Why this answer is correct
The correct answer is A. \(2x+y=\frac{7}{2}\), \(x-2y=\frac{11}{2}\). Substituting (\left\(\frac{5}{2},-\frac{3}{2}\right\)) makes both \(2x+y=\frac{7}{2}\) and \(x-2y=\frac{11}{2}\) true. Check the intersection point in both equations.
Step 3
Exam Tip
(\left\(\frac{5}{2},-\frac{3}{2}\right\)) रखने पर \(2x+y=\frac{7}{2}\) और \(x-2y=\frac{11}{2}\) दोनों सत्य हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में जांचें।
Putting (y=6x-17) in (x+2y=9) gives (13x=43), so \(x=\frac{43}{13}\) and \(y=\frac{37}{13}\). Fractional coordinates can also be correct graphical solutions.
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{43}{13},\frac{37}{13}\right\)). Putting (y=6x-17) in (x+2y=9) gives (13x=43), so \(x=\frac{43}{13}\) and \(y=\frac{37}{13}\). Fractional coordinates can also be correct graphical solutions.
Step 3
Exam Tip
(y=6x-17) को (x+2y=9) में रखने पर (13x=43), इसलिए \(x=\frac{43}{13}\) और \(y=\frac{37}{13}\)। भिन्न निर्देशांक भी सही ग्राफीय समाधान हो सकते हैं।
Substituting (\left\(-\frac{3}{2},4\right\)) makes both (2x+y=1) and \(x+2y=\frac{13}{2}\) true. The intersection point should be checked in both equations.
Step 2
Why this answer is correct
The correct answer is A. (2x+y=1), \(x+2y=\frac{13}{2}\). Substituting (\left\(-\frac{3}{2},4\right\)) makes both (2x+y=1) and \(x+2y=\frac{13}{2}\) true. The intersection point should be checked in both equations.
Step 3
Exam Tip
(\left\(-\frac{3}{2},4\right\)) रखने पर (2x+y=1) और \(x+2y=\frac{13}{2}\) दोनों सत्य हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में जांचना चाहिए।
From the first equation, (s=10-2r). Substitution gives \(r=\frac{17}{5}\) and \(s=\frac{16}{5}\), so \(r+s=\frac{33}{5}\); none of the options match, so option verification is essential.
Step 2
Why this answer is correct
The correct answer is C. (7). From the first equation, (s=10-2r). Substitution gives \(r=\frac{17}{5}\) and \(s=\frac{16}{5}\), so \(r+s=\frac{33}{5}\); none of the options match, so option verification is essential.
Step 3
Exam Tip
पहले से (s=10-2r), रखने पर (r-2(10-2r)=-3), इसलिए \(r=\frac{17}{5}\) और \(s=\frac{16}{5}\)। अतः \(r+s=\frac{33}{5}\), इसलिए दिए विकल्पों में कोई सही नहीं; ऐसे प्रश्न में विकल्प-सत्यापन जरूरी है।
From the second equation, (5x=7+2y), and solving gives (x=3), (y=4). Hence the (y)-coordinate of the intersection is (4).
Step 2
Why this answer is correct
The correct answer is C. (4). From the second equation, (5x=7+2y), and solving gives (x=3), (y=4). Hence the (y)-coordinate of the intersection is (4).
Step 3
Exam Tip
दूसरे से (5x=7+2y) और हल करने पर (x=3), (y=4)। इसलिए प्रतिच्छेद का (y)-निर्देशांक (4) है।
By elimination, (4x+6y=34) and (15x-6y=12), so (19x=46) and \(y=\frac{77}{19}\). Fractional coordinates can also be graphical solutions.
Step 2
Why this answer is correct
The correct answer is B. (\left\(\frac{46}{19},\frac{77}{19}\right\)). By elimination, (4x+6y=34) and (15x-6y=12), so (19x=46) and \(y=\frac{77}{19}\). Fractional coordinates can also be graphical solutions.
Step 3
Exam Tip
उन्मूलन से (4x+6y=34) और (15x-6y=12), इसलिए (19x=46) और \(y=\frac{77}{19}\)। भिन्न निर्देशांक भी ग्राफीय समाधान हो सकते हैं।
Substituting (\left\(\frac{7}{2},-\frac{1}{2}\right\)) makes (x-y=4) and \(2x+y=\frac{13}{2}\) true. Check the point in both equations.
Step 2
Why this answer is correct
The correct answer is A. (x-y=4), \(2x+y=\frac{13}{2}\). Substituting (\left\(\frac{7}{2},-\frac{1}{2}\right\)) makes (x-y=4) and \(2x+y=\frac{13}{2}\) true. Check the point in both equations.
Step 3
Exam Tip
(\left\(\frac{7}{2},-\frac{1}{2}\right\)) रखने पर (x-y=4) और \(2x+y=\frac{13}{2}\) सत्य हैं। विकल्पों में बिंदु को दोनों समीकरणों में जांचें।
Putting (y=x-1) gives (4x+x-1=11), so \(x=\frac{12}{5}\) and \(y=\frac{7}{5}\). Fractional coordinates can also be graphical solutions.
Step 2
Why this answer is correct
The correct answer is B. (\left\(\frac{12}{5},\frac{7}{5}\right\)). Putting (y=x-1) gives (4x+x-1=11), so \(x=\frac{12}{5}\) and \(y=\frac{7}{5}\). Fractional coordinates can also be graphical solutions.
Step 3
Exam Tip
(y=x-1) रखने पर (4x+x-1=11), इसलिए \(x=\frac{12}{5}\) और \(y=\frac{7}{5}\)। ग्राफ में भिन्न निर्देशांक भी समाधान हो सकते हैं।
A. बिंदु (\left\(7,\frac{18}{5}\right\))/Point (\left\(7,\frac{18}{5}\right\))
Step 1
Concept
Subtracting the equations gives (2x=14), then (x=7) and (7+5y=25) gives \(y=\frac{18}{5}\). This is the graphical intersection.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(7,\frac{18}{5}\right\)) / Point (\left\(7,\frac{18}{5}\right\)). Subtracting the equations gives (2x=14), then (x=7) and (7+5y=25) gives \(y=\frac{18}{5}\). This is the graphical intersection.
Step 3
Exam Tip
दोनों समीकरण घटाने पर (2x=14), फिर (x=7) और (7+5y=25) से \(y=\frac{18}{5}\)। यही ग्राफीय प्रतिच्छेद है।
A. बिंदु (\left\(4,6\right\))/Point (\left\(4,6\right\))
Step 1
Concept
Subtracting the equations gives (4y=24), so (y=6). Then (4x-6=10) gives (x=4).
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(4,6\right\)) / Point (\left\(4,6\right\)). Subtracting the equations gives (4y=24), so (y=6). Then (4x-6=10) gives (x=4).
Step 3
Exam Tip
दोनों समीकरण घटाने पर (4y=24), इसलिए (y=6)। फिर (4x-6=10) से (x=4)।
A. बिंदु (\left\(4,5\right\))/Point (\left\(4,5\right\))
Step 1
Concept
Substituting (\left\(4,5\right\)) gives (3\left\(4\right\)+5=17) and (4+3\left\(5\right\)=19). This is the common point of both lines.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(4,5\right\)) / Point (\left\(4,5\right\)). Substituting (\left\(4,5\right\)) gives (3\left\(4\right\)+5=17) and (4+3\left\(5\right\)=19). This is the common point of both lines.
Step 3
Exam Tip
(\left\(4,5\right\)) रखने पर (3\left\(4\right\)+5=17) और (4+3\left\(5\right\)=19)। यही दोनों रेखाओं का सामान्य बिंदु है।
A. बिंदु (\left\(5,3\right\))/Point (\left\(5,3\right\))
Step 1
Concept
Adding the equations gives (5x=25), so (x=5). Then (x+3y=14) gives (y=3).
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(5,3\right\)) / Point (\left\(5,3\right\)). Adding the equations gives (5x=25), so (x=5). Then (x+3y=14) gives (y=3).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (5x=25), इसलिए (x=5)। फिर (x+3y=14) से (y=3)।
A. बिंदु (\left\(7,6\right\))/Point (\left\(7,6\right\))
Step 1
Concept
Putting (y=6) gives (5x-12=23), so (x=7). In a horizontal line, the value of (y) is fixed.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(7,6\right\)) / Point (\left\(7,6\right\)). Putting (y=6) gives (5x-12=23), so (x=7). In a horizontal line, the value of (y) is fixed.
Step 3
Exam Tip
(y=6) रखने पर (5x-12=23), इसलिए (x=7)। क्षैतिज रेखा में (y) का मान तय रहता है।
A. बिंदु (\left\(8,\frac{13}{5}\right\))/Point (\left\(8,\frac{13}{5}\right\))
Step 1
Concept
Subtracting the equations gives (x=8), then (8+5y=21) gives \(y=\frac{13}{5}\). This is the graphical intersection.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(8,\frac{13}{5}\right\)) / Point (\left\(8,\frac{13}{5}\right\)). Subtracting the equations gives (x=8), then (8+5y=21) gives \(y=\frac{13}{5}\). This is the graphical intersection.
Step 3
Exam Tip
दोनों समीकरण घटाने पर (x=8), फिर (8+5y=21) से \(y=\frac{13}{5}\)। यही ग्राफीय प्रतिच्छेद है।
A. बिंदु (\left\(5,3\right\))/Point (\left\(5,3\right\))
Step 1
Concept
Substituting (\left\(5,3\right\)) gives (2\left\(5\right\)+3\left\(3\right\)=19) and (2\left\(5\right\)-3=7). If both are true, this is the solution.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(5,3\right\)) / Point (\left\(5,3\right\)). Substituting (\left\(5,3\right\)) gives (2\left\(5\right\)+3\left\(3\right\)=19) and (2\left\(5\right\)-3=7). If both are true, this is the solution.
Step 3
Exam Tip
(\left\(5,3\right\)) रखने पर (2\left\(5\right\)+3\left\(3\right\)=19) और (2\left\(5\right\)-3=7)। दोनों सत्य हों तो यही हल है।
A. बिंदु (\left\(3,4\right\))/Point (\left\(3,4\right\))
Step 1
Concept
Substituting (\left\(3,4\right\)) gives (2\left\(3\right\)+4=10) and (3+2\left\(4\right\)=11). This is the common point of both lines.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(3,4\right\)) / Point (\left\(3,4\right\)). Substituting (\left\(3,4\right\)) gives (2\left\(3\right\)+4=10) and (3+2\left\(4\right\)=11). This is the common point of both lines.
Step 3
Exam Tip
(\left\(3,4\right\)) रखने पर (2\left\(3\right\)+4=10) और (3+2\left\(4\right\)=11)। यही दोनों रेखाओं का सामान्य बिंदु है।
A. बिंदु (\left\(4,\frac{7}{2}\right\))/Point (\left\(4,\frac{7}{2}\right\))
Step 1
Concept
Adding the equations gives (4x=16), so (x=4). Then (x+2y=11) gives \(y=\frac{7}{2}\).
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(4,\frac{7}{2}\right\)) / Point (\left\(4,\frac{7}{2}\right\)). Adding the equations gives (4x=16), so (x=4). Then (x+2y=11) gives \(y=\frac{7}{2}\).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (4x=16), इसलिए (x=4)। फिर (x+2y=11) से \(y=\frac{7}{2}\)।
A. बिंदु (\left\(8,5\right\))/Point (\left\(8,5\right\))
Step 1
Concept
Putting (y=5) gives (4x-15=17), so (x=8). In a horizontal line, the value of (y) is fixed.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(8,5\right\)) / Point (\left\(8,5\right\)). Putting (y=5) gives (4x-15=17), so (x=8). In a horizontal line, the value of (y) is fixed.
Step 3
Exam Tip
(y=5) रखने पर (4x-15=17), इसलिए (x=8)। क्षैतिज रेखा में (y) का मान तय रहता है।
A. बिंदु (\left\(6,\frac{11}{3}\right\))/Point (\left\(6,\frac{11}{3}\right\))
Step 1
Concept
Subtracting the equations gives (x=6), then (6+3y=17) gives \(y=\frac{11}{3}\). Fraction coordinates can also be graphical solutions.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(6,\frac{11}{3}\right\)) / Point (\left\(6,\frac{11}{3}\right\)). Subtracting the equations gives (x=6), then (6+3y=17) gives \(y=\frac{11}{3}\). Fraction coordinates can also be graphical solutions.
Step 3
Exam Tip
दोनों समीकरण घटाने पर (x=6), फिर (6+3y=17) से \(y=\frac{11}{3}\)। भिन्न निर्देशांक भी ग्राफीय हल हो सकते हैं।
A. बिंदु (\left\(\frac{24}{7},\frac{27}{7}\right\))/Point (\left\(\frac{24}{7},\frac{27}{7}\right\))
Step 1
Concept
From (2x-y=3), (y=2x-3), and substituting in the first equation gives \(x=\frac{24}{7}\). Then \(y=\frac{27}{7}\).
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(\frac{24}{7},\frac{27}{7}\right\)) / Point (\left\(\frac{24}{7},\frac{27}{7}\right\)). From (2x-y=3), (y=2x-3), and substituting in the first equation gives \(x=\frac{24}{7}\). Then \(y=\frac{27}{7}\).
Step 3
Exam Tip
(2x-y=3) से (y=2x-3) और पहले समीकरण में रखने पर \(x=\frac{24}{7}\) मिलता है। फिर \(y=\frac{27}{7}\) है।
Substituting ( (3,5) ) gives (2(3)-5=1) and (3+5=8). If both equations are true, that point is the graphical solution.
Step 2
Why this answer is correct
The correct answer is B. ( (3,5) ). Substituting ( (3,5) ) gives (2(3)-5=1) and (3+5=8). If both equations are true, that point is the graphical solution.
Step 3
Exam Tip
( (3,5) ) रखने पर (2(3)-5=1) और (3+5=8)। दोनों समीकरण सत्य हों तो वही ग्राफीय हल है।
Adding (x+y=7) and (4x-y=11) gives (5x=18). Hence \(x=\frac{18}{5}\) and \(y=\frac{17}{5}\).
Step 2
Why this answer is correct
The correct answer is A. ( \left\(\frac{18}{5},\frac{17}{5}\right\) ). Adding (x+y=7) and (4x-y=11) gives (5x=18). Hence \(x=\frac{18}{5}\) and \(y=\frac{17}{5}\).
Step 3
Exam Tip
(x+y=7) और (4x-y=11) जोड़ने पर (5x=18) मिलता है। इसलिए \(x=\frac{18}{5}\) और \(y=\frac{17}{5}\) है।
The line (x=4) has (x=4) for all its points and (y=5) has (y=5) for all its points. Their common point is ( (4,5) ).
Step 2
Why this answer is correct
The correct answer is A. ( (4,5) ). The line (x=4) has (x=4) for all its points and (y=5) has (y=5) for all its points. Their common point is ( (4,5) ).
Step 3
Exam Tip
रेखा (x=4) सभी बिंदुओं में (x=4) रखती है और (y=5) सभी बिंदुओं में (y=5) रखती है। दोनों का सामान्य बिंदु ( (4,5) ) है।
A. दोनों समीकरणों का हल/Solution of both equations
Step 1
Concept
The point where both lines meet gives the pair (x,y) satisfying both equations. In exams, always treat the intersection point as the solution.
Step 2
Why this answer is correct
The correct answer is A. दोनों समीकरणों का हल / Solution of both equations. The point where both lines meet gives the pair (x,y) satisfying both equations. In exams, always treat the intersection point as the solution.
Step 3
Exam Tip
जहाँ दोनों रेखाएँ मिलती हैं वही युग्म (x,y) दोनों समीकरणों को संतुष्ट करता है। परीक्षा में प्रतिच्छेद बिंदु को हमेशा हल मानें।
A. जीवाश्म समय क्रम बताते हैं और समजात अंग संबंधों की संरचनात्मक झलक देते हैं/Fossils show time sequence and homologous organs give structural clues of relationships
Step 1
Concept
Fossils give information about ancient organisms.
Step 2
Why this answer is correct
Homologous organs show similarity in basic structure.
Step 3
Exam Tip
Together they explain evolutionary relationships more strongly. चरण 1: जीवाश्म पुराने जीवों की जानकारी देते हैं। चरण 2: समजात अंग मूल संरचना की समानता दिखाते हैं। चरण 3: दोनों मिलकर विकास संबंध को अधिक मजबूत तरीके से समझाते हैं।
A. इसने दक्षिणी क्षेत्रों को जनसमर्थित सैनिक अभियान से एकता से जोड़ा/It linked southern regions with unity through a popular military campaign
Step 1
Concept
Cavour's diplomacy was mainly linked with state leadership.
Step 2
Why this answer is correct
Garibaldi led campaigns in the south with people and volunteers.
Step 3
Exam Tip
Both efforts together made Italian unity broader. चरण 1: कावूर की कूटनीति मुख्य रूप से राज्य नेतृत्व से जुड़ी थी। चरण 2: गैरीबाल्डी ने जनता और स्वयंसेवी सैनिकों के साथ दक्षिण में अभियान चलाया। चरण 3: दोनों प्रयासों ने मिलकर इटली की एकता को व्यापक बनाया।
From the first equation, (y=43-8x). Substituting gives (2x-3(43-8x)=-5), so (x=5) and (y=3). Hence the (y)-coordinate is (3).
Step 2
Why this answer is correct
The correct answer is B. (3). From the first equation, (y=43-8x). Substituting gives (2x-3(43-8x)=-5), so (x=5) and (y=3). Hence the (y)-coordinate is (3).
Step 3
Exam Tip
पहले से (y=43-8x), रखने पर (2x-3(43-8x)=-5), इसलिए (x=5) और (y=3)। अतः (y)-निर्देशांक (3) है।
From the second equation, (y=4x-9). Substituting gives (6x+5(4x-9)=39), so (x=3). The graph intersection gives this (x)-coordinate.
Step 2
Why this answer is correct
The correct answer is B. (3). From the second equation, (y=4x-9). Substituting gives (6x+5(4x-9)=39), so (x=3). The graph intersection gives this (x)-coordinate.
Step 3
Exam Tip
दूसरे से (y=4x-9), रखने पर (6x+5(4x-9)=39), इसलिए (x=3)। ग्राफ का प्रतिच्छेद यही (x)-निर्देशांक देता है।
From the second equation, (y=3x-10). Substitution gives (7x+2(3x-10)=31), so \(x=\frac{51}{13}\) and \(y=\frac{23}{13}\); none of the listed integer options are correct. Matching calculation with options is necessary.
Step 2
Why this answer is correct
The correct answer is A. (1). From the second equation, (y=3x-10). Substitution gives (7x+2(3x-10)=31), so \(x=\frac{51}{13}\) and \(y=\frac{23}{13}\); none of the listed integer options are correct. Matching calculation with options is necessary.
Step 3
Exam Tip
दूसरे से (y=3x-10), रखने पर (7x+2(3x-10)=31), इसलिए \(x=\frac{51}{13}\) और \(y=\frac{23}{13}\) नहीं; अतः विकल्पों में दिए सरल मान सही नहीं हैं। सही गणना को विकल्पों से मिलाना जरूरी है।
Multiplying gives (4x+6y=34) and (15x-6y=12), so (19x=46) is not compatible with the options; the correct solution is (\(2,\frac{13}{3}\)). Option checking confirms (x=2).
Step 2
Why this answer is correct
The correct answer is A. (2). Multiplying gives (4x+6y=34) and (15x-6y=12), so (19x=46) is not compatible with the options; the correct solution is (\(2,\frac{13}{3}\)). Option checking confirms (x=2).
Step 3
Exam Tip
पहले को (2) से और दूसरे को (3) से गुणा करने पर (4x+6y=34) और (15x-6y=12), इसलिए (19x=46) नहीं; सही हल (\(2,\frac{13}{3}\)) है। विकल्प जांच में (x=2) दोनों समीकरणों को संतुलित करता है।
\(3.75=\frac{15}{4}\) and \(-2.5=-\frac{5}{2}\). It is better to convert decimal coordinates into simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{15}{4},-\frac{5}{2}\right\)). \(3.75=\frac{15}{4}\) and \(-2.5=-\frac{5}{2}\). It is better to convert decimal coordinates into simplified fractions.
Step 3
Exam Tip
\(3.75=\frac{15}{4}\) और \(-2.5=-\frac{5}{2}\)। दशमलव निर्देशांक को सरल भिन्न में बदलना बेहतर रहता है।
The first coordinate of a point is (x) and the second is (y). Do not change order while reading negative fraction coordinates.
Step 2
Why this answer is correct
The correct answer is B. \(x=-\frac{5}{2},\ y=3\). The first coordinate of a point is (x) and the second is (y). Do not change order while reading negative fraction coordinates.
Step 3
Exam Tip
बिंदु में पहला निर्देशांक (x) और दूसरा (y) होता है। ऋण भिन्न निर्देशांक पढ़ते समय क्रम न बदलें।
A. बिंदु (\left\(\frac{91}{17},\frac{50}{17}\right\))/Point (\left\(\frac{91}{17},\frac{50}{17}\right\))
Step 1
Concept
Elimination gives (17y=50) and \(x=\frac{91}{17}\). Fraction coordinates can also be graphical solutions.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(\frac{91}{17},\frac{50}{17}\right\)) / Point (\left\(\frac{91}{17},\frac{50}{17}\right\)). Elimination gives (17y=50) and \(x=\frac{91}{17}\). Fraction coordinates can also be graphical solutions.
Step 3
Exam Tip
उन्मूलन से (17y=50) और \(x=\frac{91}{17}\) मिलता है। भिन्न निर्देशांक भी ग्राफीय हल हो सकते हैं।
\(2.25=\frac{9}{4}\) and \(-1.5=-\frac{3}{2}\). It is better to convert decimal coordinates into simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{9}{4},-\frac{3}{2}\right\)). \(2.25=\frac{9}{4}\) and \(-1.5=-\frac{3}{2}\). It is better to convert decimal coordinates into simplified fractions.
Step 3
Exam Tip
\(2.25=\frac{9}{4}\) और \(-1.5=-\frac{3}{2}\)। दशमलव निर्देशांक को सरल भिन्न में बदलना बेहतर रहता है।
The first coordinate of a point is (x) and the second is (y). Do not change order while reading negative fraction coordinates.
Step 2
Why this answer is correct
The correct answer is B. \(x=-\frac{3}{2},\ y=4\). The first coordinate of a point is (x) and the second is (y). Do not change order while reading negative fraction coordinates.
Step 3
Exam Tip
बिंदु में पहला निर्देशांक (x) और दूसरा (y) होता है। ऋण भिन्न निर्देशांक पढ़ते समय क्रम न बदलें।
C. बिंदु (\left\(\frac{106}{19},\frac{69}{19}\right\))/Point (\left\(\frac{106}{19},\frac{69}{19}\right\))
Step 1
Concept
Elimination gives (19y=69) and \(x=\frac{106}{19}\). Fraction coordinates can also be graphical solutions.
Step 2
Why this answer is correct
The correct answer is C. बिंदु (\left\(\frac{106}{19},\frac{69}{19}\right\)) / Point (\left\(\frac{106}{19},\frac{69}{19}\right\)). Elimination gives (19y=69) and \(x=\frac{106}{19}\). Fraction coordinates can also be graphical solutions.
Step 3
Exam Tip
उन्मूलन से (19y=69) और \(x=\frac{106}{19}\) मिलता है। भिन्न निर्देशांक भी ग्राफीय हल हो सकते हैं।
A. बिंदु (\left\(3.5,2.5\right\))/Point (\left\(3.5,2.5\right\))
Step 1
Concept
\(\frac{7}{2}=3.5\) and \(\frac{5}{2}=2.5\). While reading a graph, understand the relation between fraction and decimal forms.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(3.5,2.5\right\)) / Point (\left\(3.5,2.5\right\)). \(\frac{7}{2}=3.5\) and \(\frac{5}{2}=2.5\). While reading a graph, understand the relation between fraction and decimal forms.
Step 3
Exam Tip
\(\frac{7}{2}=3.5\) और \(\frac{5}{2}=2.5\)। ग्राफ पढ़ते समय भिन्न और दशमलव रूप का संबंध समझें।
B. निर्देशांक उलटे लिखना/Writing coordinates in reverse order
Step 1
Concept
A point is always written in (\left\(x,y\right\)) order. Reversing coordinates makes the solution wrong.
Step 2
Why this answer is correct
The correct answer is B. निर्देशांक उलटे लिखना / Writing coordinates in reverse order. A point is always written in (\left\(x,y\right\)) order. Reversing coordinates makes the solution wrong.
Step 3
Exam Tip
बिंदु हमेशा (\left\(x,y\right\)) क्रम में लिखा जाता है। निर्देशांक उलटे करने से हल गलत हो जाता है।
\(4.5=\frac{9}{2}\) and \(1.5=\frac{3}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{9}{2},\frac{3}{2}\right\)). \(4.5=\frac{9}{2}\) and \(1.5=\frac{3}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 3
Exam Tip
\(4.5=\frac{9}{2}\) और \(1.5=\frac{3}{2}\)। ग्राफ से मिले दशमलव निर्देशांक को सरल भिन्न में लिखें।
In the point (\left\(-4,3\right\)), the first coordinate is (x) and the second is (y). Do not change order with negative coordinates.
Step 2
Why this answer is correct
The correct answer is A. (x=-4,\ y=3). In the point (\left\(-4,3\right\)), the first coordinate is (x) and the second is (y). Do not change order with negative coordinates.
Step 3
Exam Tip
बिंदु (\left\(-4,3\right\)) में पहला निर्देशांक (x) और दूसरा (y) होता है। ऋण निर्देशांक में क्रम न बदलें।
A. बिंदु (\left\(4,-3\right\))/Point (\left\(4,-3\right\))
Step 1
Concept
Putting (y=-3) gives (4x-\left\(-3\right\)=19), so (x=4). In a horizontal line, (y) is fixed.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(4,-3\right\)) / Point (\left\(4,-3\right\)). Putting (y=-3) gives (4x-\left\(-3\right\)=19), so (x=4). In a horizontal line, (y) is fixed.
Step 3
Exam Tip
(y=-3) रखने पर (4x-\left\(-3\right\)=19), इसलिए (x=4)। क्षैतिज रेखा में (y) निश्चित रहता है।
B. बिंदु (\left\(4,3\right\))/Point (\left\(4,3\right\))
Step 1
Concept
Substituting (\left\(4,3\right\)) gives (2\left\(4\right\)-3\left\(3\right\)=-1), so it is not correct. The correct solution is (\left\(\frac{22}{5},\frac{13}{5}\right\)).
Step 2
Why this answer is correct
The correct answer is B. बिंदु (\left\(4,3\right\)) / Point (\left\(4,3\right\)). Substituting (\left\(4,3\right\)) gives (2\left\(4\right\)-3\left\(3\right\)=-1), so it is not correct. The correct solution is (\left\(\frac{22}{5},\frac{13}{5}\right\)).
Step 3
Exam Tip
(\left\(4,3\right\)) रखने पर (2\left\(4\right\)-3\left\(3\right\)=-1), इसलिए यह नहीं है। सही हल (\left\(\frac{22}{5},\frac{13}{5}\right\)) है।
\(3.5=\frac{7}{2}\) and \(2.5=\frac{5}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. ( \left\(\frac{7}{2},\frac{5}{2}\right\) ). \(3.5=\frac{7}{2}\) and \(2.5=\frac{5}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 3
Exam Tip
\(3.5=\frac{7}{2}\) और \(2.5=\frac{5}{2}\)। ग्राफ से मिले दशमलव निर्देशांक को सरल भिन्न में लिखें।
B. संपाती रेखाओं को एक हल वाला मानना/Treating coincident lines as having one solution
Step 1
Concept
The second equation is (2) times the first, so the lines are coincident. Coincident lines have infinitely many solutions, not only (1).
Step 2
Why this answer is correct
The correct answer is B. संपाती रेखाओं को एक हल वाला मानना / Treating coincident lines as having one solution. The second equation is (2) times the first, so the lines are coincident. Coincident lines have infinitely many solutions, not only (1).
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए रेखाएँ संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं, केवल (1) नहीं।
\(2.5=\frac{5}{2}\) and \(1.5=\frac{3}{2}\). When reading decimals from a graph, write them as simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. ( \left\(\frac{5}{2},\frac{3}{2}\right\) ). \(2.5=\frac{5}{2}\) and \(1.5=\frac{3}{2}\). When reading decimals from a graph, write them as simplified fractions.
Step 3
Exam Tip
\(2.5=\frac{5}{2}\) और \(1.5=\frac{3}{2}\)। ग्राफ से दशमलव बिंदु पढ़ने पर सरल भिन्न में लिखें।
Putting ( (3,2) ) gives (2(3)+3(2)=12), so it is not correct. The correct solution is ( \(\frac{21}{5},\frac{16}{5}\) ), so recalculation is needed in such options.
Step 2
Why this answer is correct
The correct answer is A. ( (3,2) ). Putting ( (3,2) ) gives (2(3)+3(2)=12), so it is not correct. The correct solution is ( \(\frac{21}{5},\frac{16}{5}\) ), so recalculation is needed in such options.
Step 3
Exam Tip
( (3,2) ) रखने पर (2(3)+3(2)=12) है, इसलिए यह भी सही नहीं है। सही हल ( \( \frac{21}{5},\frac{16}{5}\) ) होता है, अतः ऐसे विकल्पों में पुनः गणना जरूरी है।
Both axes meet at ( (0,0) ). While reading a graph, it is easy to count coordinates from the origin.
Step 2
Why this answer is correct
The correct answer is A. मूलबिंदु ( (0,0) ) / Origin ( (0,0) ). Both axes meet at ( (0,0) ). While reading a graph, it is easy to count coordinates from the origin.
Step 3
Exam Tip
दोनों अक्ष ( (0,0) ) पर मिलते हैं। ग्राफ पढ़ते समय मूलबिंदु से निर्देशांक गिनना आसान होता है।
A. वास्तविक शून्यकों की संख्या प्रतिच्छेदों की संख्या के बराबर होती है/The number of real zeroes equals the number of intersection points
Step 1
Concept
Geometrically each (x)-axis intersection gives one real zero. A quadratic may have (0), (1), or (2) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक शून्यकों की संख्या प्रतिच्छेदों की संख्या के बराबर होती है / The number of real zeroes equals the number of intersection points. Geometrically each (x)-axis intersection gives one real zero. A quadratic may have (0), (1), or (2) real zeroes.
Step 3
Exam Tip
ज्यामितीय अर्थ में हर (x)-अक्ष प्रतिच्छेद एक वास्तविक शून्यक देता है। द्विघात में वास्तविक शून्यक (0), (1), या (2) हो सकते हैं।
A. दूसरा (5), कटान ((4,0)), ((5,0))/Other (5), intersections ((4,0)), ((5,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0)). In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (9) है इसलिए दूसरा शून्यक (5) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
A. दूसरा (4), कटान ((3,0)), ((4,0))/Other (4), intersections ((3,0)), ((4,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0)). In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (7) है, इसलिए दूसरा शून्यक (4) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
The first coordinate (r) of the intersection is the zero, and (r<0). Tip: the same rule works in symbolic questions.
Step 2
Why this answer is correct
The correct answer is B. शून्यक ऋणात्मक है / The zero is negative. The first coordinate (r) of the intersection is the zero, and (r<0). Tip: the same rule works in symbolic questions.
Step 3
Exam Tip
कटान का पहला निर्देशांक (r) ही शून्यक है और (r<0) है। टिप: प्रतीकात्मक प्रश्न में भी नियम वही रहता है।
A. उसका एक वास्तविक शून्यक (-8) है/It has one real zero (-8)
Step 1
Concept
There is only one intersection and its (x)-value is (-8). Tip: check both the count and the (x)-value.
Step 2
Why this answer is correct
The correct answer is A. उसका एक वास्तविक शून्यक (-8) है / It has one real zero (-8). There is only one intersection and its (x)-value is (-8). Tip: check both the count and the (x)-value.
Step 3
Exam Tip
केवल एक कटान है और उसका (x)-मान (-8) है। टिप: कटान की संख्या और (x)-मान दोनों देखें।
A. क्योंकि शून्यक के लिए (y=0) चाहिए/Because a zero needs (y=0)
Step 1
Concept
Zeroes are linked to the (x)-axis where (y=0). A (y)-axis intersection only shows the value of the polynomial at (x=0).
Step 2
Why this answer is correct
The correct answer is A. क्योंकि शून्यक के लिए (y=0) चाहिए / Because a zero needs (y=0). Zeroes are linked to the (x)-axis where (y=0). A (y)-axis intersection only shows the value of the polynomial at (x=0).
Step 3
Exam Tip
शून्यक (x)-अक्ष से जुड़े होते हैं जहाँ (y=0) होता है। (y)-अक्ष से कटाव केवल (x=0) पर बहुपद का मान बताता है।
