Question

Solve graphically the following system of linear equations. Also, find the coordinates of the points where the lines meet axis of y:

x + 2y = 6

3x – 2y = 2

Answer 1

1. Points for line 1: x + 2y = 6

We can express x in terms of y:

x = 6 – 2y

When y = 0, x = 6 ⇒ (6, 0)

When y = 2, x = 2 ⇒ (2, 2)

When y = 3, x = 0 ⇒ (0, 3)

x	6	2	0
y	0	2	3

2. Points for line 2: 3x – 2y = 2

We can express y in terms of x:

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

When x = 0, y = –1 ⇒ (0, –1)

When x = 2, y = 2 ⇒ (2, 2)

When x = 4, y = 5 ⇒ (4, 5)

x	0	2	4
y	–1	2	5

Graphical representation

The two plotted lines intersect at a single point, which provides the solution to the system.

Solution of the system: x = 2, y = 2 or (2, 2)

Intersection points on the y-axis: (0, 3) for the first line and (0, –1) for the second line.