Question

Find the solution to the system of linear equations y = 5x + 4 and y = −3x + 12 using the intersection method. Check your answer.

(x, y) =

Answer 1

The solution to the system of linear equations is (1,9).

Explanation:

The given system of linear equations

`y=5x+4` ... (1)

`y=-3x+12` .... (2)

Subtract equation (2) from equation (1) to eliminate y.

`y-y=(5x+4)-(-3x+12)`

`0=5x+4+3x-12`

On combining like terms, we get

`0=(5x+3x)+(4-12)`

`0=8x-8`

Add 8 on both sides.

`0+8=8x-8+8`

`8=8x`

Divide both sides by 8.

`1=x`

The value of x is 1.

Substitute x=1 in equation (1).

`y=5(1)+4`

`y=5+4`

`y=9`

The value of y is 9.

Therefore the solution to the system of linear equations is (1,9).