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, yaxis):
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 yaxis. 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 .