Find the solution to the system of equations by substitution.
-x + 7y = -2 3x + y = 34
A) (3, 7)
B) (7, 12)
C) (12, -2)
D) (-2, 3)

Question

Quizplus · Accepted Answer

First, solve one of the equations for one variable in terms of the other. From the second equation, $3x + y = 34$, we can solve for $y$: $y = 34 - 3x$. Substitute this expression for $y$ in the first equation: $x + 7(34 - 3x) = -2$. Simplify and solve for $x$: $x + 238 - 21x = -2$, which simplifies to $-20x = -240$, so $x = 12$. Substitute $x = 12$ back into $y = 34 - 3x$ to find $y$: $y = 34 - 3(12) = 34 - 36 = -2$. Therefore, the solution is $x = 12$, $y = -2$, which corresponds to choice C.

Find the Solution to the System of Equations by Substitution