Question

Becca graphs the equations y = –3(x – 1) and y = x – 5 to solve the equation –3(x – 1) = x – 5. Her graph is shown below.

Answer 1

we have

$y=-3(x-1)$ ------> equation A

$y=x-5$ ------> equation B

we know that

The intersection point both graphs is the solution of the system of linear equations

Using a graphing tool

see the attached figure

the solution is the point $(2,-3)$  

Alternative Method

Becca equate equation A and equation B

$-3(x-1)=x-5$

Eliminate the parenthesis left side

$-3x+3=x-5$

$4x=8$

$x=2$

Find the value of y

Substitute the value of x in the equation A or B

$y=2-5=-3$

the solution is the point $(2,-3)$