Question

Solve the system of equations.

y = −3x + 4
y = 3x − 2

Group of answer choices

x = -2

x = 1

x = -1

x = 2

Answer 1

To solve the system of equations given:

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

We can set the equations equal to each other since they both equal \( y \):

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

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

1. Add \( 3x \) to both sides:
\[
4 = 6x - 2
\]

2. Add \( 2 \) to both sides:
\[
6 = 6x
\]

3. Divide both sides by \( 6 \):
\[
x = 1
\]

Now, we can substitute \( x = 1 \) back into one of the original equations to find \( y \). Let's use the first equation:

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

So, the solution to the system of equations is:

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

From the answer choices provided, the value of \( x \) is:

\[
\text{x = 1}
\]