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 start with the two equations:

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

### Step 1: Substitute Equation 1 into Equation 2

From Equation 1, we already have \( y \) expressed in terms of \( x \). We can substitute this expression for \( y \) into Equation 2.

Substituting \( y = -2x + 1 \) into Equation 2 gives us:

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

### Step 2: Simplify the Equation

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 we rearrange the equation to isolate \( x \):

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

\[
-8x = 8
\]

Now divide by -8:

\[
x = -1
\]

### Step 4: Substitute back to find y

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

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

\[
y = 2 + 1 = 3
\]

### Conclusion

The solution to the system of equations is:

\[
(x, y) = (-1, 3)
\]

So the final answer is:

\[
(-1, 3)
\]