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GG.8 Solve a system of equations using substitution

J8X
Solve using substitution.

y = –x + 8
y = –10x − 10

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1 answer

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

  1. \( y = -x + 8 \)
  2. \( y = -10x - 10 \)

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

\[ -x + 8 = -10x - 10 \]

Now, let's solve for \( x \):

  1. Add \( 10x \) to both sides:

\[ -x + 10x + 8 = -10 \]

This simplifies to:

\[ 9x + 8 = -10 \]

  1. Subtract 8 from both sides:

\[ 9x = -10 - 8 \]

This simplifies to:

\[ 9x = -18 \]

  1. Divide both sides by 9:

\[ x = -2 \]

Now, we will substitute \( x = -2 \) back into one of the original equations to find \( y \). Let's use the first equation \( y = -x + 8 \):

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

This simplifies to:

\[ y = 2 + 8 = 10 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (-2, 10) \]

So the final answer is:

\[ \boxed{(-2, 10)} \]