GG.8 Solve a system of equations using substitution

Question

J8X
Solve using substitution.

y = –8x + 10
y = 10x − 8

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Answer 1

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

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

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

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

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

1. Add \( 8x \) to both sides: \[ 10 = 18x - 8 \]

2. Add \( 8 \) to both sides: \[ 10 + 8 = 18x \] \[ 18 = 18x \]

3. Divide both sides by \( 18 \): \[ x = 1 \]

Now that we have \( x = 1 \), we can substitute this value back into one of the original equations to find \( y \). We can use the first equation:

\[ y = -8(1) + 10 \] \[ y = -8 + 10 \] \[ y = 2 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (1, 2) \]

Therefore, the final answer is:

\[ \boxed{(1, 2)} \]