Question

Solve the system of equations graphed on the coordinate axes below.
y, equals, minus, 3, x
y=
−3x
y, equals, 5, x, plus, 8
y=
5x+8

Answer 1

To solve the system of equations given by

1. \( y = -3x \)
2. \( y = 5x + 8 \)

we can set the two equations equal to each other because they both equal \( y \):

\[
-3x = 5x + 8
\]

Now, we'll solve for \( x \):

1. Add \( 3x \) to both sides:

\[
0 = 8x + 8
\]

2. Subtract \( 8 \) from both sides:

\[
-8 = 8x
\]

3. Divide by \( 8 \):

\[
x = -1
\]

Now that we have the value of \( x \), we can substitute it back into either equation to find the corresponding \( y \)-value. We'll use the first equation:

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

Therefore, the solution to the system of equations, or the point of intersection, is

\[
(x, y) = (-1, 3)
\]

So, the solution is \( (-1, 3) \).