Ask a New Question
Menu

Solve the system of equations using substitution.

y=2x+2


y=3x+6


(4 points)
(
,
)

1 answer

To solve the system of equations using substitution, we have the following equations:

  1. \( y = 2x + 2 \)
  2. \( y = 3x + 6 \)

Since both equations are equal to \( y \), we can set them equal to each other:

\[ 2x + 2 = 3x + 6 \]

Now, we will solve for \( x \).

  1. Subtract \( 2x \) from both sides: \[ 2 = x + 6 \]

  2. Subtract \( 6 \) from both sides: \[ 2 - 6 = x \] \[ -4 = x \]

Now that we have \( x = -4 \), we can substitute this value back into one of the original equations to find \( y \). Let's use the first equation:

\[ y = 2(-4) + 2 \] \[ y = -8 + 2 \] \[ y = -6 \]

Thus, the solution to the system of equations is: \[ (x, y) = (-4, -6) \]

In coordinate form: \[ \boxed{(-4, -6)} \]