Question

Solve the following equations graphically :
x + 3y = 8
3x = 2 + 2y

Answer 1

x + 3y = 8
3x = 2 + 2y
x + 3y = 8 ________(1)
3x = 2 + 2y _______(2)
Now, x + 3y = 8

⇒ y = `(8 - x)/(3)`
Corresponding values of x and y can be tabulated as :

x	-1	2	5
y	3	2	1

Plotting points (-1, 3), (2, 2), (5, 1) and joiniing them, we get a line I, which is the graph of equation (1).
Again, 3x = 2 + 2y

⇒ x = `(2x + 2y)/(3)`
Corresponding values of x and y can be tabulated as :

x	2	4	0
y	2	5	-1

Plotting points (2, 2), (4, 5), (0, -1) and joining them, we get a line I₂ which is the graph of equation (2).

The two lines I₂ and I₂ intersect at the point (2, 2). Hence, x = 2, y = 2 is the unique solution of the given equation.