Question

Draw the graph of the following lines:

4x + 3y = 12 and 2x − 3y = 6

Find the solution set and the area of triangle formed by the two lines with y-axis.

Answer 1

4x + 3y = 12

2x − 3y = 6

The lines intersect at the point (3, 0).

This is the solution to the system of equations.

The triangle is formed between:

The y-intercepts of both lines:

y = 4

y = −2

so, Base = |4 − 2| = 2

Base = |4 − (−2)|

= |4 + 2|

= 6

Height = 3 

Area = `1/2  xx "base" xx "height"`

Area = `1/2 xx 6 xx 3`

9 square units