Question

Solve the following equations graphically :
3y = 5 - x
2x = y + 3

Answer 1

3y = 5 - x
2x = y + 3
3y = 5 - x _________(1)
2x = y + 3 ________(2)

3y = 5 - x
⇒ y = `(5 - x)/(3)`
Corresponding values of x and y can be tabulated as :

x	2	-1	-4
y	1	2	3

Plotting points (2, 1), (-1, 2), (-4, 3) and joining them, we get a line l₁ which is the graph of equation (1).
Again, 2x = y + 3

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

x	2	1	3
y	1	-1	3

Plotting point (2, 1), (-1, 1), (3, 3) and joining them, we get a line l₂ which is the graph of equation (2).

The two lines l₁ and l₂ intersect at a unique point (2, 1).
Thus, x = 2 and y = 1 is the unique solution of the given equations.