Question

Solve using substitution.

y = 3x − 4
y = –2x + 1

Answer 1

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

1. \( y = 3x - 4 \)
2. \( y = -2x + 1 \)

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

\[
3x - 4 = -2x + 1
\]

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

1. Add \( 2x \) to both sides:

\[
3x + 2x - 4 = 1
\]

This simplifies to:

\[
5x - 4 = 1
\]

2. Next, add \( 4 \) to both sides:

\[
5x = 5
\]

3. Now, divide by \( 5 \):

\[
x = 1
\]

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

\[
y = 3(1) - 4
\]

This simplifies to:

\[
y = 3 - 4 = -1
\]

So the solution to the system of equations is:

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

**Final Answer: (1, -1)**