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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 two lines have slopes (m_1=-\frac{4}{3}) and (m_2=-\frac{4}{3}), but different (y)-intercepts, what is the graphical conclusion?Which conclusion is correct for the lines (3x-y=2) and (6x-2y=5)?Which pair shows a consistent and dependent pair on the graph?What is the solution of \(2x-y=6\) and \(x+2y=8\) on the graph?If (3x+2y=p) and (6x+4y=20) give infinitely many solutions, what is (p)?For which value will (5x+2y=13) and (10x+4y=k) have no solution?At which point do the lines x + y = 11 and 2x − 3y = −3 intersect on the graph?Two lines meet at (A(1,4)) on a graph. Which pair verifies this?What will be the graph of (4x+6y=18) and (2x+3y=10)?If (ax+6y=18) and (2x+3y=9) are coincident lines, what is the value of (a)?Which of the following pairs has its lines intersecting on the y-axis?Which point does not lie on the line \(2x+7y=14\)?If the lines (2x+3y=12) and (4x+my=24) are coincident, what is (m)?What is the (y)-coordinate of the intersection of (3x+4y=25) and (5x-2y=7)?A farmer has (42) plants of two types, and the first type is (8) more than the second. What will be the graphical solution?Let x and y be two numbers. Three times their sum is 60 and twice their difference is 12; that is, 3x + 3y = 60 and 2x − 2y = 12. What is the solution (x, y) obtained by the graphical method?Which pair will give a unique solution because of different slopes?If (x+ky=8) and (2x+6y=16) give infinitely many solutions, what is the value of (k)?What is the solution of (4x+y=19) and (x-2y=-7) on the graph?If the graph of a pair shows two coincident lines, how can the solution be described?