To solve the system of equations using the substitution method, we'll first substitute the expression for \( x \) from the second equation into the first equation:
Given:
1) \( -2x + 8y = 16 \)
2) \( x = 4y - 8 \)
Substitute equation 2 into equation 1:
\[ -2(4y - 8) + 8y = 16 \]
Now, let's simplify and solve for \( y \):
\[ -8y + 16 + 8y = 16 \]
\[ 16 = 16 \]
This equation simplifies to \( 16 = 16 \), which is always true. This means that the value of \( y \) can be anything.
Now, let's solve for \( x \) using equation 2:
\[ x = 4y - 8 \]
Since \( y \) can be any value, let's choose \( y = 0 \) for simplicity:
\[ x = 4(0) - 8 \]
\[ x = -8 \]
So, the solution to the system of equations is \( x = -8 \) and \( y \) can be any real number.
