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Subjects

Mathematics

Graphical method of finding solutions.

ग्राफीय विधि से हल ज्ञात करना

In this Class 10 Mathematics topic from the chapter Pair of Linear Equations in Two Variables, students learn to represent each linear equation as a straight line on the Cartesian plane and identify the solution through the point where the lines intersect. The topic explains how intersecting, parallel, and coincident lines correspond to a unique solution, no solution, or infinitely many solutions. Students also practise plotting points, reading coordinates, and checking solutions graphically.

Practice questions

Which point lies on both lines (2x+y=9) and (x-y=3)?If (2x+5y=20) and (4x+10y=40) are graphed, how many actually distinct lines will be visible?What type of lines are (9x-6y=21) and (3x-2y=7)?Two lines intersect at ((-3,2)) on a graph. Which pair of equations is correct?If (2x+3y=5) and (4x+6y=10), which statement about the solution set is correct?When the line \(6x+2y=18\) is written in the form \(y=mx+c\), what is its slope \(m\)?In which pair do both lines have equal slopes but different (y)-intercepts?If the graph of (x+2y=7) and (3x+6y=21) is drawn, which point will be a solution?What is the graphical conclusion for (x-3y=2) and (2x-6y=9)?In a shop, the total cost of two items is (90), and the first item is (14) costlier than the second. What is the graphical solution?If the lines (4x+ay=16) and (8x+10y=32) are coincident, what is the value of (a)?For which value will (x+4y=12) and (2x+8y=k) be distinct parallel lines?If the only intersection of two lines is ((r,s)) and (2r+s=10), (r-2s=-3), what is (r+s)?If the graphical solution of (3x+y=14) and (x-y=2) is ((p,q)), what is (p-q)?How will the lines (2x+7y=14) and (4x+14y=31) appear on a graph?If (5x+ky=20) and (15x+6y=60) are coincident lines, what is the value of (k)?At which point will the lines (3x+2y=18) and (x-y=1) meet on the graph?For which value will the lines (4x+ay=16) and (8x+10y=35) be distinct and parallel?If the intersection of two lines on a graph is \(\left(-\frac{3}{2},4\right)\), which pair can be correct?Which intercept pair is correct for drawing the line (7x-3y=21)?