Question

Solve the following system of equations graphically
x - y + 1 = 0
4x + 3y = 24

Answer 1

x - y + 1 = 0   ...(1)
4x + 3y = 24  ...(2)

x - y + 1 = 0
⇒ y = x + 1
Corresponding values of x and y can be tabulated as :

x	0	3	-1
y	1	4	0

Plotting points (0, 1), (1, 2), (-1, 0) and joining them, we get a line l₁ which is the graph of equation (1).

4x + 3y = 24
⇒ x = ${\displaystyle \frac{24-3y}{4}}$
Corresponding values of x and y can be tabulated as :

x	6	3	0
y	0	4	8

Plotting points (6, 0), (3, 4), (0, 8) and joining them, we get a line l₂ which is the graph of equation (2).

The lines l₁ and l₂ intersect at (3, 4). Thus, x = 3 and y = 4 is the unique solution of equation (1) and (2).
Now, from the graph, it can be seen that the  lines l₁, and l₂
Intersect the x-axis at points (-1, 0) and (6, 0).