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. what are the solution(s) of –3(x – 1) = x – 5? a) –5 and 3 b) –3 c) 1 and 5 d) 2

Remark

A pair of linear equations have only ONE solution. Not only that, but the solution is a point and is of the form (x , y)

Solution

- 3(x - 1) = x - 5                     Remove the brackets.

- 3x + 3 = x - 5                      Subtract x from both sides.

- 3x - x + 3 = - 5                    Combine

- 4x + 3 = - 5                         Subtract 3 from both sides.

-4x + 3 -  3 = - 5 - 3               Combine

-4x = - 8                                Divide by - 4

-4x/ -4  = -8/-4                    

x = 2

y = x - 5

y = 2 - 5

y = - 3

So the point is (2 , - 3)

the "answer" you want is D. But it is not a solution.

my guess would be b and d, but i didn’t actually get out the pen and paper. lol