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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 (a_1=5,\ b_1=10,\ c_1=15) and (a_2=1,\ b_2=2,\ c_2=3), how will the lines be?If (a_1=2,\ b_1=-4,\ c_1=9) and (a_2=1,\ b_2=-2,\ c_2=4), what is the correct conclusion?Which pair of equations is consistent and independent?For the line \(x-3y=12\), what intercepts are obtained at \(x=0\) and \(y=0\)?If the intersection point is read as \(\left(2.25,-1.5\right)\) on a graph, what is its fraction form?What is the intersection point of \(2x+y=10\) and \(x+2y=11\)?At which point do the lines \(5x-y=13\) and \(x+2y=16\) intersect on the graph?Which value table is correct for the line (4x+y=16)?If the points \\((-1,7)\\) and \\( (2,1)\\) are included in a value table of a line, which is the correct equation of the line?What is the correct statement about (x+2y=6) and (2x+4y=20) on the graph?In which situation can reading the graphical solution exactly be most difficult?At which point do the lines \(2x+3y=19\) and \(2x-y=7\) meet?What is the correct intersection point of \(2x+3y=19\) and \(2x-y=7\)?If the pair of linear equations \(x+y=8\) and \(kx+2y=14\) passes through the point \((2,6)\), what is the value of \(k\)?If the point of intersection of the lines \(2x+ay=16\) and \(x+y=7\) is \((2,5)\), what is the value of \(a\)?Which equation will represent a coincident line with \(x+2y=9\)?Which line will be parallel and distinct to (2x-3y=6)?On a graph, two paths are shown by \(3x+2y=18\) and \(x+2y=10\). Where will they meet?In a park, two paths are represented by \(2x+5y=29\) and \(x+5y=21\). What is their intersection point?Which point lies on both lines \(x-2y=-5\) and \(2x+y=13\)?