Question

solve the system by substitution.
$y = 8x + 32$
$y = -8x$

Explanation:

Step1: Substitute \( y = -8x \) into \( y = 8x + 32 \)

Since both equations are solved for \( y \), we can set them equal to each other. So substitute \( y \) in the first equation with \( -8x \) from the second equation:
\( -8x = 8x + 32 \)

Step2: Solve for \( x \)

Subtract \( 8x \) from both sides:
\( -8x - 8x = 8x + 32 - 8x \)
\( -16x = 32 \)
Divide both sides by \( -16 \):
\( x = \frac{32}{-16} = -2 \) Wait, the initial answer had \( x = 2 \), that was a mistake. Let's correct it. Wait, let's redo step 2.

Wait, starting over. Step1: Substitute \( y = -8x \) into \( y = 8x + 32 \), so:

\( -8x = 8x + 32 \)

Subtract \( 8x \) from both sides:

\( -8x - 8x = 32 \)

\( -16x = 32 \)

Divide both sides by \( -16 \):

\( x = \frac{32}{-16} = -2 \)

Step3: Find \( y \) using \( y = -8x \)

Substitute \( x = -2 \) into \( y = -8x \):

\( y = -8(-2) = 16 \)

Wait, the initial answer was wrong. Let's do it correctly.

Wait, the system is \( y = 8x + 32 \) and \( y = -8x \).

Set \( -8x = 8x + 32 \)

\( -8x - 8x = 32 \)

\( -16x = 32 \)

\( x = 32 / (-16) = -2 \)

Then \( y = -8*(-2) = 16 \)

So the correct solution is \( (-2, 16) \). The initial answer in the image had a mistake. Let's present the correct steps.

(Correct Version):

Step1: Substitute \( y = -8x \) into \( y = 8x + 32 \)

Since \( y \) is expressed as \( -8x \) in the second equation, substitute this into the first equation:
\( -8x = 8x + 32 \)

Step2: Solve for \( x \)

Subtract \( 8x \) from both sides:
\( -8x - 8x = 32 \)
\( -16x = 32 \)
Divide by \( -16 \):
\( x = \frac{32}{-16} = -2 \)

Step3: Find \( y \) using \( y = -8x \)

Substitute \( x = -2 \) into \( y = -8x \):
\( y = -8(-2) = 16 \)

Answer:

The solution to the system is \( \boldsymbol{(-2, 16)} \) (the initial answer in the image was incorrect; the correct solution is found by proper substitution and solving).