Question

Use substitution to solve the system of equations.

y = 4.5x + 7.5
y = –3.5x – 4.5
x = –1.5, y = –0.75
x = 1.5, y = 0.75
x = 1.5, y = –0.75
x = –1.5, y = 0.75

Answer 1

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

1. \( y = 4.5x + 7.5 \)
2. \( y = -3.5x - 4.5 \)

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

\[
4.5x + 7.5 = -3.5x - 4.5
\]

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

1. Add \( 3.5x \) to both sides:

\[
4.5x + 3.5x + 7.5 = -4.5
\]

This simplifies to:

\[
8x + 7.5 = -4.5
\]

2. Subtract \( 7.5 \) from both sides:

\[
8x = -4.5 - 7.5
\]

This gives:

\[
8x = -12
\]

3. Divide by 8:

\[
x = -\frac{12}{8} = -1.5
\]

Now that we have \( x = -1.5 \), we can find \( y \) using either equation. We'll use the first equation:

\[
y = 4.5(-1.5) + 7.5
\]

Calculating that:

\[
y = -6.75 + 7.5 = 0.75
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-1.5, 0.75)
\]

Now, let's check this result against the possible answers provided:

- \( (x, y) = (-1.5, -0.75) \)
- \( (x, y) = (1.5, 0.75) \)
- \( (x, y) = (1.5, -0.75) \)
- \( (x, y) = (-1.5, 0.75) \)

The correct solution is:

\[
x = -1.5, y = 0.75
\]

So the correct answer is \( (x, y) = (-1.5, 0.75) \).