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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

A library has (58) books of two types, and the first type is (12) more than the second. What will be the graphical solution?For the two variables x and y, the equations \(2x+2y=72\) and \(3x-3y=18\) are given. What is the point of intersection of the graphs of these two linear equations?Which pair will give a unique solution because of different coefficient ratios?If (2x+ky=18) and (6x+12y=54) give infinitely many solutions, what is the value of (k)?What is the solution of (5x+y=27) and (2x-3y=-6) on the graph?If the graph of a pair shows two intersecting lines, how can the solution be described?Which point lies on both lines \(3x+y=14\) and \(x-2y=-5\)?If (4x+9y=36) and (8x+18y=72) are graphed, how many distinct lines will be visible?What type of lines are (12x+15y=30) and (4x+5y=10)?Two lines intersect at ((-2,-3)) on a graph. Which pair of equations is correct?If (5x+6y=30) and (10x+12y=60), which statement about the solution set is correct?When the line \\(8x-4y=16\\) is written in the form \\(y=mx+c\\), what is its slope \\(m\\)?If the graph of (2x+3y=18) and (6x+9y=54) is drawn, which point will be a solution?What is the graphical conclusion for (2x-5y=7) and (4x-10y=16)?In a shop, the total cost of two items is (126), and the first item is (18) costlier than the second. What is the graphical solution?If the lines (6x+ay=30) and (18x+12y=90) are coincident, what is the value of (a)?For which value will (3x+7y=21) and (6x+14y=k) be distinct parallel lines?If the graphical intersection point of the lines \(4x-y=11\) and \(x+y=4\) is \((p,q)\), what is the value of \(p-q\)?If the lines (7x+by=21) and (14x+10y=50) are distinct parallel lines, what will be the value of (b)?At which point will the lines \(5x+2y=23\) and \(x-3y=-4\) meet on the graph?