Question

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

Answer 1

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

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

Since we already have \( y \) in terms of \( x \) from the first equation, we can substitute this expression for \( y \) into the second equation.

### Step 1: Substitute \( y \)

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

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

### Step 2: Simplify

Now, simplify the right-hand side:

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

### Step 3: Solve for \( x \)

Now add \( 4x \) to both sides:

\[
-4x + 4x = 4x + 4x + 8
\]
\[
0 = 8x + 8
\]

Now, isolate \( x \):

\[
-8 = 8x
\]
\[
x = -1
\]

### Step 4: Substitute back to find \( y \)

Now that we have \( x = -1 \), substitute it back into the first equation to solve for \( y \):

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

### Final Solution

The solution to the system of equations is:
\[
(x, y) = (-1, 3)
\]

Thus, the final answer is:
\[
\boxed{(-1, 3)}
\]