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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

If the lines \(x+ay=10\) and \(2x-y=5\) intersect at the point \((3,1)\), what is the value of \(a\)?If the lines \(kx+2y=14\) and \(x+y=6\) intersect at the point \((2,4)\), what is the value of \(k\)?If \(\left(6,-2\right)\) is mistakenly read as \(\left(-2,6\right)\) on a graph, what type of mistake is it?Two routes are represented by \(3x+y=20\) and \(x+y=12\). At which point will the routes meet?If the line represented by the equation \(2x+ay=18\) is coincident with the line \(2x+3y=18\), what is the value of \(a\)?For (x+by=7) to be parallel and distinct to (2x+6y=18), which value of (b) is suitable?Which point is correct for \(3x-4y=12\) and can be useful for drawing the graph?If two lines intersect at \(\left(\frac{5}{2},\frac{7}{2}\right)\) on a graph, what will be the value of (x+y)?If the line (kx+3y=15) is parallel and distinct to the line (2x+6y=18), what will be the value of (k)?At which point do the lines \(3x+2y=19\) and \(x-y=1\) meet on the graph?What is the point of intersection of the graphs of \(4x-y=9\) and \(2x+3y=23\), that is, their graphical solution?At which point will the lines \(5x+3y=31\) and \(x+y=7\) intersect?What is the intersection point of \(2x-5y=-4\) and \(3x+y=19\)?If (a_1=6,\ b_1=-9,\ c_1=12) and (a_2=2,\ b_2=-3,\ c_2=5), what will be the position of the lines?How will the graphs of (8x-12y=20) and (2x-3y=5) be?What is the correct pair of x-intercept and y-intercept of the line \\(9x-5y=45\\)?At which point will the lines \(x=-5\) and \(4x-3y=7\) meet?What is the point of intersection of the lines \(y=6\) and \(5x-2y=23\)?What is the graphical intersection point of the lines \(x+3y=14\) and \(4x-3y=11\)?Where do the lines \(6x+5y=39\) and \(x-5y=-14\) meet?