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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 \(x-3y=-8\) and \(3x+y=20\)?If the lines \(kx+4y=22\) and \(x+y=6\) intersect at the point \((2,4)\), what is the value of \(k\)?If \(\left(7,-3\right)\) is mistakenly read as \(\left(-3,7\right)\) on a graph, what type of mistake is it?Two routes are represented by \(4x+y=26\) and \(x+y=14\). At which point will the routes meet?For (x+by=8) to be parallel and distinct to (3x+12y=30), which value of (b) is suitable?Which point is correct for \(5x-6y=30\) and can be useful for drawing the graph?If two lines intersect at \(\left(\frac{7}{2},\frac{9}{2}\right)\) on a graph, what will be the value of (x+y)?If the line (kx-2y=7) is parallel and distinct to the line (3x-6y=12), what will be the value of (k)?At which point do the lines \(2x+7y=31\) and \(x-y=1\) meet?Which is the correct pair of intercepts of the line \(8x-3y=24\)?Which pair of equations will be inconsistent on the graph?Which point lies on both lines \(3x-2y=4\) and \(x+4y=22\)?If the intersection point on the graph is \(\left(-\frac{7}{3},\frac{2}{3}\right)\), what will be the value of (x-y)?On a graph, two paths are shown by \(2x+5y=34\) and \(x+5y=26\). Where will they meet?If the two lines (2x+3y=12) and (4x+6y=18) are drawn on a graph, what is the correct conclusion about their solution?How will the lines (3x-2y=6) and (6x-4y=12) appear on a graph?Which point is the intersection of the lines (x+y=7) and (x-y=1) on a graph?If the graph of two lines is (y=2x+1) and (y=2x-5), what type of solution will they have?At which point will the lines (x=5) and (y=-3) meet on a graph?How many solutions will be obtained from the graphs of (2x-y=1) and (4x-2y=2)?