Question

Solve the following system of equations graphically:

3x + 2y = 12, x – y + 1= 0

Answer 1

1. Find points for the first line: 3x + 2y = 12

We can rewrite this equation in terms of y:

`y = (12 - 3x)/2`

If x = 0, y = `(12 - 0)/2` = 6 → (0, 6)

If x = 4, y = `(12 - 12)/2` = 0 → (4, 0)

If x = 2, y = `(12 - 6)/2` = 3 → (2, 3)

2. Find points for the second line: x – y + 1 = 0

We can rewrite this equation as: y = x + 1

If x = 0, y = 0 + 1 = 1 → (0, 1)

If x = –1, y = –1 + 1 = 0 → (–1, 0)

If x = 2, y = 2 + 1 = 3 → (2, 3)

Graphical Representation

By plotting both lines on the coordinate plane, they clearly intersect at the point (2, 3).

Therefore, the unique solution to the system is x = 2, y = 3.