# Graphical Method

## Pair Of Linear Equations In Two Variables of Class 10 ### GRAPHICAL SOLUTION OF LINEAR EQUATIONS IN TWO VARIABLES:

Graphs of the type (i) ax = b:

question 1. Draw the graphs of the following equations:

(i) x = 2, (ii) 2x = 1 (iii) x + 4 = 0 (iv) x = 0

Solution:

 (i) x = 2 (ii) 2x = 1 ⇒ x = 1/2 (iii) x + 4 = 0 ⇒ x = –4 (iv) x = 0 Graphs of the type (ii) ay = b:

1. Draw the graphs of the following equations: (i) y = 0, (ii) y - 2 = 0, (iii) 2y + 4 = 0

 (i) y = 0 (ii) y – 2 = 0 (iii) 2y + 4 = 0 ⇒ y = –2 Graphs of the type (iii) ax + by = 0 (Passing through origin):

question 1. Draw the graphs of the following: (i) x = y, (ii) x = –y

Solution: (i) x – y

 x 1 4 –3 0 y 1 4 –3 0

(ii) x = –y

 x 1 –2 0 y –1 2 0 Graphs of the Type (iv) ax + by + c = 0. (Making Interception x - axis, y-axis):

question 1. Solve the following system of linear equations graphically: x - y = 1, 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also determine this area.

Solution: (i) x – y = 1

x – y + 1

 x 0 1 2 y –1 0 1

(ii) 2x + y = 8

(ii) 2 x + y = 8

y = 8 – 2x X 0 1 2 Y 8 6 4

Solution is x = 3 and y = 2

Area of is x = 3 and y = 2

Area of ΔABC = 1/2 × BC × AD

= 1/2 × 9 × 3 = 13.5 Sq. unit.

### NATURE OF GRAPHICAL SOLUTION:

Let equations of two lines are a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0.

(i) Lines are consistent (unique solution) i.e. they meet at one point condition is . (ii) Lines are inconsistent (no solution) i.e. they do not meet at one point condition is . (iii) Lines are coincident (infinite solution) i.e. overlapping lines (or they are on one another) condition is . 