Question

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the first equation is substituted into the second equation.

−x + 5y = 1
2x + 4y = −4

Choices:

2(5y − 1) + 4y = −4
2(−5y + 1) + 4y = −4
2x + 4(−5y + 1) = −4
2x + 4(5y − 1) = −4

Answer 1

First, you need to isolate the x in the first equation.
-x + 5y = 1
Subtract 5y from both sides, leaving you with the following equation:
-x = 1-5y
Because you are trying to solve for positive x and not negative x, you need to make x positive. Therefore you divide both sides by -1. In Algebra, when 1 is the coefficient of the variable, it is not shown, but it is still there. The new equation will be the following: x = 5y-1
Now you just need to substitute the x within the second equation for the x equation we just solved for.

Therefore, the right answer will be 2(5y-1)+4y= -4. Now, all you have to do is choose the answer that states exactly that, which is the first choice.