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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

When the equations \(3x-2y=4\) and \(x+5y=23\) are represented graphically, which is their point of intersection, i.e. their graphical solution?At which point will the lines \(5x+2y=16\) and \(3x-4y=2\) intersect?What is the intersection point of \(2x-5y=-7\) and \(3x+2y=24\)?If (a_1=4,\ b_1=-6,\ c_1=10) and (a_2=2,\ b_2=-3,\ c_2=7), what will be the position of the lines?How will the graphs of (6x-9y=15) and (2x-3y=5) be?Which pair of equations will give no solution on the graph?Which is the correct ordered pair of the x-intercept and y-intercept of the line \(7x-4y=28\), respectively?At which point will the lines \(x=-4\) and \(3x-2y=10\) meet?What is the point of intersection of the lines \(y=5\) and \(4x-3y=17\)?If for two lines (\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}), which conclusion is correct?If (\frac{a_1}{a_2}\ne\frac{b_1}{b_2}), which statement is correct in graphical method?For the pair of linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), which statement about their graphs is correct?What is the point of intersection of the graphs of the lines \(x+2y=11\) and \(3x-2y=5\)?Where do the lines \(5x+6y=30\) and \(x-2y=-6\) meet?Which point lies on \(2x+5y=27\) but not on \(x+y=9\)?A student writes only one solution for (2x+3y=12) and (4x+6y=24). What is the mistake?If the intersection point on the graph is \(\left(-\frac{3}{2},4\right)\), what is the correct solution?Which statement is correct for the graphs of (3x-2y=6) and (6x-4y=18)?What is the point of intersection of the lines \(2x+3y=18\) and \(y=0\)?Using the graphical method, what is the point of intersection of the lines \\(4x-5y=20\\) and \\(x=0\\)?