Question

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

Answer 1

To solve the system of equations using the substitution method, we start with the given equations:

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

Since Equation 1 already expresses \( y \) in terms of \( x \), we can substitute \( y \) from Equation 1 into Equation 2.

First, let's rearrange Equation 2:

\[
-4x = -2y + 10
\]

Now, substitute \( y \) from Equation 1 into Equation 2:

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

Simplifying the right side:

\[
-4x = 4x - 2 + 10
\]

Combining like terms:

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

Next, we add \( 4x \) to both sides:

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

This yields:

\[
0 = 8x + 8
\]

Subtracting 8 from both sides gives:

\[
-8 = 8x
\]

Dividing both sides by 8 results in:

\[
x = -1
\]

Now that we have the value of \( x \), we can substitute it back into Equation 1 to find \( y \):

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

Calculating this gives:

\[
y = 2 + 1 = 3
\]

Thus, the solution to the system of equations is:

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