To solve the system of equations using the substitution method, we start with the two given equations:
- \( y = -2x + 1 \) (Equation 1)
- \( -4x = -2y + 10 \) (Equation 2)
First, we can substitute \( y \) from Equation 1 into Equation 2.
Starting with Equation 2:
\[ -4x = -2y + 10 \]
Now, substitute \( y \) from Equation 1:
\[ -4x = -2(-2x + 1) + 10 \]
Now, simplify the right side:
\[ -4x = 4x - 2 + 10 \] \[ -4x = 4x + 8 \]
Next, let's add \( 4x \) to both sides to combine like terms:
\[ 0 = 8x + 8 \]
Now, we can isolate \( x \):
\[ 8x = -8 \] \[ x = -1 \]
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ y = -2(-1) + 1 \] \[ y = 2 + 1 \] \[ y = 3 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-1, 3) \]
In conclusion, the solution is \((-1, 3)\).