Use the substitution method to solve the system of equations. Choose the correct ordered pair.

2x + 2y= 16
y= x-4
• A. (6, -2)
• в. (2,2)
C. (6,2)
D. (2, -2)

1 answer

To solve the system of equations using the substitution method, we'll start with the two equations:

  1. \( 2x + 2y = 16 \)
  2. \( y = x - 4 \)

We can substitute the expression for \( y \) from the second equation into the first equation.

  1. Substitute \( y \) in the first equation:

\[ 2x + 2(x - 4) = 16 \]

  1. Simplify this equation:

\[ 2x + 2x - 8 = 16 \] \[ 4x - 8 = 16 \]

  1. Add 8 to both sides:

\[ 4x = 24 \]

  1. Divide by 4:

\[ x = 6 \]

  1. Now substitute \( x = 6 \) back into the second equation to find \( y \):

\[ y = 6 - 4 = 2 \]

The solution to the system of equations is \( (x, y) = (6, 2) \).

Thus, the correct ordered pair is:

C. (6, 2)