Question

Vince successfully solved the system of equations

-5x + y = -21
y = x - 1

Which of these statments could correctly describe what he did?

Answer 1

Answer: Choice B

Replace y with x-1 in the first equation.

Solve for x to get x = 5, which leads to y = 4.

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Step-by-step explanation:

Since y = x-1, we can replace every copy of y with x-1 and solve for x.

This is the substitution step. Think of it like a substitute teacher replacing your regular teacher on a temporary basis.

-5x + y = -21

-5x + (x-1) = -21

-4x -1 = -21

-4x = -21+1

-4x = -20

x = -20/(-4)

x = 5 is the first part of the solution

Then this leads to:

y = x-1

y = 5-1

y = 4 as the second part of the solution

Overall the solution as an ordered pair is (x,y) = (5, 4).

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If you wanted, you could plug x = 5 into the first equation and solve for y like so:

-5x+y = -21

-5(5)+y = -21

-25+y = -21

y = -21+25

y = 4

But it's preferable to use y = x-1 since it's more direct.