linear-equations se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
1257 questions tagged with linear-equations.
If (ax+9y=27) and (14x+21y=64) have no solution then what will (a) be?
C. (6)
कोई हल नहीं के लिए (a/14=9/21) और (27/64) अलग होना चाहिए। इसलिए (a=6)। / For no solution (a/14=9/21) and (27/64) must be different. Therefore (a=6).
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What is the correct conclusion for (9x+5y-28=0) and (18x+11y-56=0)?
C. एक अद्वितीय हलOne unique solution
यहां \(9/18 \ne 5/11\) इसलिए रेखाएं एक बिंदु पर कटती हैं। ऐसी स्थिति में एक अद्वितीय हल मिलता है। / Here \(9/18 \ne 5/11\) so the lines intersect at one point. In this case one unique solution is obtained.
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What is the correct ratio relation for (8x-3y+22=0) and (16x-6y+47=0)?
A. (816=(-3) / (-6) \ne 22 / 47)
पहले दो अनुपात बराबर हैं और तीसरा अलग है। इसलिए कोई हल नहीं होगा। / The first two ratios are equal and the third is different. Therefore there will be no solution.
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Which ratio relation is correct for (4x+9y-31=0) and (12x+27y-93=0)?
C. (412=9 / 27=(-31) / (-93))
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं। / Here all three ratios are equal. Therefore both lines are coincident and have infinitely many solutions.
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What is the correct description of the graph of (2x+11y=27) and (5x+19y=46)?
C. एक बिंदु पर कटती रेखाएंLines intersecting at one point
यहां \(2/5 \ne 11/19\) इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा। / Here \(2/5 \ne 11/19\) so the lines will intersect at one point. This gives one unique solution.
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What will be shown in the graph of (15x+10y=40) and (3x+2y=8)?
A. एक ही रेखाSame line
पहला समीकरण दूसरे का (5) गुना है। इसलिए दोनों समीकरण एक ही रेखा दिखाते हैं। / The first equation is (5) times the second. Therefore both equations show the same line.
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Which statement is correct about the graph of (14x+21y=49) and (2x+3y=8)?
C. रेखाएं अलग समानांतर हैंLines are distinct parallel
यहां (14/2=21/3) लेकिन (49/8) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी। / Here (14/2=21/3) but (49/8) is different. Therefore the graph will show distinct parallel lines.
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What will (b) be for (bx+8y=32) and (12x+24y=71) to have no solution?
B. (4)
कोई हल नहीं के लिए (b/12=8/24) और (32/71) अलग होना चाहिए। इसलिए (b=4)। / For no solution (b/12=8/24) and (32/71) must be different. Hence (b=4).
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What will (a) be for (5x+ay=35) and (15x+18y=105) to have infinitely many solutions?
C. (6)
अनंत हल के लिए (5/15=a/18=35/105) होना चाहिए। इससे (a=6) मिलता है। / For infinitely many solutions (5/15=a/18=35/105) must hold. This gives (a=6).
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Which condition is correct for (6x+ky=24) and (3x+5y=17) to have a unique solution?
B. \(k \ne 10\)
अद्वितीय हल के लिए \(6/3 \ne k/5\) होना चाहिए। इसलिए \(k \ne 10\) सही शर्त है। / For a unique solution \(6/3 \ne k/5\) must hold. Therefore \(k \ne 10\) is the correct condition.
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What will (q) be for (7x+qy=29) and (14x+10y=58) to have infinitely many solutions?
C. (5)
दूसरा समीकरण पहले का (2) गुना है इसलिए (q/10=1/2) होना चाहिए। अतः (q=5)। / The second equation is (2) times the first so (q/10=1/2) must hold. Hence (q=5).
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What is the value of (p) for (px+6y=18) and (10x+15y=45) to have infinitely many solutions?
B. (3)
अनंत हल के लिए (p/10=6/15=18/45) होना चाहिए। इसलिए (p=3)। / For infinitely many solutions (p/10=6/15=18/45) must hold. Therefore (p=3).
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If \(a_1/a_2=b_1/b_2 \ne c_1/c_2\) then which situation will occur in the graph?
C. अलग समानांतर रेखाएंDistinct parallel lines
पहले दो अनुपात बराबर और तीसरा अलग हो तो रेखाएं समानांतर और अलग होती हैं। इसलिए कोई सामान्य हल नहीं मिलता। / If the first two ratios are equal and the third differs the lines are parallel and distinct. Therefore no common solution is obtained.
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If \(a_1/a_2=b_1/b_2=c_1/c_2\) then what will be the nature of the pair of equations?
C. संगत और आश्रितConsistent and dependent
तीनों अनुपात बराबर हों तो दोनों समीकरण एक ही रेखा दर्शाते हैं। ऐसा युग्म संगत और आश्रित होता है। / If all three ratios are equal both equations represent the same line. Such a pair is consistent and dependent.
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What is the correct solution status for (4x+7y=23) and (9x+15y=48)?
B. एक अद्वितीय हलOne unique solution
यहां \(4/9 \ne 7/15\) इसलिए रेखाएं एक बिंदु पर कटती हैं। पहले दो अनुपात अलग हों तो एक अद्वितीय हल होता है। / Here \(4/9 \ne 7/15\) so the lines intersect at one point. If the first two ratios differ there is one unique solution.
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How many solutions will (9x-4y=17) and (18x-8y=39) have?
C. कोई हल नहींNo solution
यहां (9/18=(-4)/(-8)) लेकिन (17/39) अलग है। इसलिए रेखाएं समानांतर और अलग हैं। / Here (9/18=(-4)/(-8)) but (17/39) is different. Therefore the lines are parallel and distinct.
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What is the correct conclusion for (8x+3y=21) and (16x+6y=42)?
A. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं। / The second equation is (2) times the first so both lines are coincident. Coincident lines have infinitely many solutions.
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If (5x+2y=13) and (10x+4y=m) form an inconsistent pair then what is the correct condition for (m)?
C. \(m \ne 26\)
पहले दो अनुपात बराबर हैं इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 26\)। / The first two ratios are equal so the constant ratio must differ for inconsistency. Hence \(m \ne 26\).
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What is the value of (a) for (ax+4y=20) and (9x+12y=61) to have no solution?
B. (3)
कोई हल नहीं के लिए (a/9=4/12) और (20/61) अलग होना चाहिए। इससे (a=3) मिलता है। / For no solution (a/9=4/12) and (20/61) must be different. This gives (a=3).
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What is the value of (k) for (2x+5y=16) and (6x+15y=k) to have infinitely many solutions?
B. (48)
दूसरा समीकरण पहले का (3) गुना होना चाहिए इसलिए (k=48)। अनंत हल के लिए सभी अनुपात बराबर होने चाहिए। / The second equation must be (3) times the first so (k=48). For infinitely many solutions all ratios must be equal.
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C. असंगतInconsistent
पहले दो अनुपात (4/8=3/6) बराबर हैं लेकिन (125/260) अलग है। इसलिए प्रणाली असंगत है। / The first two ratios (4/8=3/6) are equal but (125/260) is different. Therefore, the system is inconsistent.
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What conclusion follows from comparing the ratios of (a) and (b) in (5x+7y=32) and (9x+13y=58)?
B. (59 \ne 7 / 13), इसलिए एक अद्वितीय हल / 13), so one unique solution
यहां \(5/9 \ne 7/13\), इसलिए रेखाएं एक बिंदु पर कटेंगी। पहले दो अनुपात अलग हों तो एक अद्वितीय हल मिलता है। / Here \(5/9 \ne 7/13\), so the lines will intersect at one point. If the first two ratios differ, one unique solution is obtained.
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What is the correct solution status for (11x-4y=26) and (22x-8y=53)?
C. कोई हल नहींNo solution
यहां (11/22=(-4)/(-8)) लेकिन (26/53) अलग है। इसलिए रेखाएं समानांतर और अलग हैं। / Here (11/22=(-4)/(-8)) but (26/53) is different. Therefore, the lines are parallel and distinct.
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What will be the value of (m) for (3x+my=24) and (12x+28y=96) to have infinitely many solutions?
C. (7)
अनंत हल के लिए (3/12=m/28=24/96) होना चाहिए। इसलिए (m=7) सही है। / For infinitely many solutions, (3/12=m/28=24/96) must hold. Therefore, (m=7) is correct.
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What is the correct solution status for (15x+4y=37) and (7x+2y=18)?
C. एक अद्वितीय हलOne unique solution
यहां \(15/7 \ne 4/2\), इसलिए रेखाएं कटेंगी। अतः एक अद्वितीय हल है। / Here \(15/7 \ne 4/2\), so the lines will intersect. Hence, there is one unique solution.
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What is the correct conclusion by observing (12x-8y=20) and (3x-2y=6)?
A. कोई हल नहींNo solution
यहां (12/3=(-8)/(-2)) लेकिन (20/6) अलग है। इसलिए रेखाएं समानांतर और अलग हैं। / Here (12/3=(-8)/(-2)) but (20/6) is different. Therefore, the lines are parallel and distinct.
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Which statement is correct by observing (9x+2y=31) and (18x+4y=62)?
B. रेखाएं एक ही हैंLines are the same
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं एक ही हैं। / The second equation is (2) times the first. Therefore, both lines are the same.
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If (lx+9y=27) and (8x+18y=55) have no solution, what will be the value of (l)?
C. (4)
कोई हल नहीं के लिए (l/8=9/18) और (27/55) अलग होना चाहिए। इसलिए (l=4)। / For no solution, (l/8=9/18) and (27/55) must be different. Hence, (l=4).
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What will (k) be for (6x+ky=42) and (2x+5y=14) to have infinitely many solutions?
B. (15)
पहला समीकरण दूसरे का (3) गुना होना चाहिए। इसलिए (k=15) है। / The first equation must be (3) times the second. Therefore, (k=15).
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What will (a) be for (3x+4y=10) and (6x+ay=25) to have no solution?
C. (8)
कोई हल नहीं के लिए (3/6=4/a) और (10/25) अलग होना चाहिए। इससे (a=8) मिलता है। / For no solution, (3/6=4/a) and (10/25) must be different. This gives (a=8).
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