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

Answer:

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

Step-by-step 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).