To solve the system of equations using substitution, we have the equations:
- \( 2x + 2y = 50 \)
- \( y = 4x \)
First, we can substitute the expression for \( y \) from the second equation into the first equation.
Substituting \( y = 4x \) into the first equation:
\[ 2x + 2(4x) = 50 \]
This simplifies to:
\[ 2x + 8x = 50 \]
Combining like terms gives us:
\[ 10x = 50 \]
Now, we solve for \( x \):
\[ x = \frac{50}{10} = 5 \]
Next, we substitute \( x = 5 \) back into the equation \( y = 4x \) to find \( y \):
\[ y = 4(5) = 20 \]
So, the solution to the system of equations is:
\[ (x, y) = (5, 20) \]