Question

Solve the system of equations graphed on the coordinate axes below. y, equals, minus, 5, x, minus, 8 y= −5x−8 y, equals, start fraction, 2, divided by, 3, end fraction, x, minus, 8 y= 3 2 ​ x−8

Answer 1

To solve the given system of equations, we have the following two equations:

1. \( y = -5x - 8 \)
2. \( y = \frac{2}{3}x - 8 \)

To find the points of intersection (the solution to the system), we can set the two equations equal to each other since both are equal to \(y\):

\[
-5x - 8 = \frac{2}{3}x - 8
\]

Next, simplify the equation. First, we can eliminate \(-8\) from both sides:

\[
-5x = \frac{2}{3}x
\]

Now, to eliminate the fraction, multiply every term by 3:

\[
-15x = 2x
\]

Next, we can add \(15x\) to both sides to isolate the \(x\) terms:

\[
0 = 17x
\]

Dividing by 17 gives us:

\[
x = 0
\]

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

\[
y = -5(0) - 8 = -8
\]

Thus, the solution to the system of equations, which is the point of intersection, is:

\[
(x, y) = (0, -8)
\]

Therefore, the final answer is:

\[
\boxed{(0, -8)}
\]