Extra Questions for Class 10 Maths Chapter 3 Linear Equations Based on Graphical Method of Solving Linear Equations

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Graphical Method of Finding Solution of a Pair of Linear Equations

To solve the pair of linear equation proceed as below.

Step 1: Draw a graph for each linear equation.

Step 2: Find the coordinate of the point of intersection of the two drawn lines.

Step 3: The coordinates of the point of intersection of the lines are the solutions of given linear equations.

>> If the lines are intersecting.

Intersecting lines have one common point. So, the pair of linear equation will have one solution.

>> If the lines are parallel.

Parallel lines have no common points. So, the pair of linear equations will have no solution.

>> If the lines are coincident.

Coincident lines have infinite common points. So, the pair of equations will have infinitely many solutions.

Q.1. Solve each of the following systems of equations graphically:

(i) 3x+2y=4, 2x-3y=7

(ii) 3x+y+1=0, 2x-3y+8=0

(iii) x+2y+2=0, 3x+2y-2=0

(iv) 2x+3y=8, x-2y+3=0

Q.2. Solve the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis:

(i) x-y+1=0, 3x+2y-12=0

(ii) x-2y+2=0, 2x+y-6=0

Q.3. Show graphically that each of the following given systems of equations has infinitely many solutions:

(i) x – 2y = 5, 3x – 6y = 15

(ii) 2x + 3y = 6, 4x + 6y = 12

Q.4. Show graphically that the following given systems of equations is inconsistent, i.e., has no solution.

2x+3y=4, 4x+6y=12

Q.5. Solve the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis.

2x-5y+4=0, 2x+y-8=0

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