Question

Use the substitution method to solve the system y=−2x+1
, −4x=−2y+10
.(1 point)

Answer 1

To solve the system of equations using the substitution method, we have the following two equations:

1. \( y = -2x + 1 \)
2. \( -4x = -2y + 10 \)

First, we can substitute the expression for \( y \) from the first equation into the second equation.

Substituting \( y = -2x + 1 \) into the second equation gives us:

\[
-4x = -2(-2x + 1) + 10
\]

Now, let's simplify the right side:

\[
-4x = -2(-2x) + (-2)(1) + 10
\]
\[
-4x = 4x - 2 + 10
\]
\[
-4x = 4x + 8
\]

Now, let's get all the \( x \) terms on one side:

\[
-4x - 4x = 8
\]
\[
-8x = 8
\]

Now, divide both sides by \(-8\):

\[
x = -1
\]

Now that we have \( x \), we can substitute this value back into the first equation to find \( y \):

\[
y = -2(-1) + 1
\]
\[
y = 2 + 1
\]
\[
y = 3
\]

So, the solution to the system of equations is:

\[
\boxed{( -1, 3 )}
\]