Solve the system of equations graphed on the coordinate axes below.

y, equals, minus, 3, x, minus, 5
y=
−3x−5
y, equals, start fraction, 4, divided by, 3, end fraction, x, minus, 5
y=
3
4

x−5

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

To solve the system of equations given by:

1. \( y = -3x - 5 \)
2. \( y = \frac{4}{3}x - 5 \)

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

\[
-3x - 5 = \frac{4}{3}x - 5
\]

To eliminate the constant term \(-5\) from both sides, we can add 5 to both sides:

\[
-3x = \frac{4}{3}x
\]

Next, we want to eliminate the fraction by multiplying the entire equation by 3 to make calculations easier:

\[
3(-3x) = 3\left(\frac{4}{3}x\right)
\]

This simplifies to:

\[
-9x = 4x
\]

Next, we add \( 9x \) to both sides:

\[
0 = 4x + 9x
\]

This simplifies to:

\[
0 = 13x
\]

Now, we divide both sides by \( 13 \):

\[
x = 0
\]

Now, we substitute \( x = 0 \) back into one of the original equations to find \( y \). We can use either equation; let’s use the first one:

\[
y = -3(0) - 5
\]

This simplifies to:

\[
y = -5
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (0, -5)
\]

Therefore, the point of intersection is \((0, -5)\).