Question

Solve the linear equations 3x + y = 14 and y = 2 graphically.

Answer 1

For 3x + y = 14:

If x = 4, then y = 14 – 3(4)

= 14 – 12

= 2

Point is (4, 2).

If x = 0, then y = 14

Point is (0, 14).

If x = 2, then y = 14 – 3(2)

= 14 – 6

= 8

Point is (2, 8).

Plotting these points and drawing the line gives a straight line.

For y = 2:

This is a line parallel to the x-axis passing through 2 on the y-axis.

Observing the graph, both lines intersect at the point where y = 2. 

Substituting y = 2 into the first equation:

3x + 2 = 14

⇒ 3x = 12

⇒ x = 4

The point of intersection is (4, 2).

The solution of the equations is x = 4, y = 2.