Question

The system of equations y=−15x−6
and y=−2x+3

the solution to the system of equations is (Response area, Response area).

Answer 1

To find the solution to the system of equations:

1. \( y = -15x - 6 \)
2. \( y = -2x + 3 \)

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

\[
-15x - 6 = -2x + 3
\]

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

1. First, add \( 15x \) to both sides:

\[
-6 = 13x + 3
\]

2. Then, subtract \( 3 \) from both sides:

\[
-6 - 3 = 13x
\]
\[
-9 = 13x
\]

3. Now divide both sides by \( 13 \):

\[
x = -\frac{9}{13}
\]

Now that we have the value of \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use the second equation \( y = -2x + 3 \):

\[
y = -2\left(-\frac{9}{13}\right) + 3
\]

Calculate:

\[
y = \frac{18}{13} + 3
\]
\[
y = \frac{18}{13} + \frac{39}{13} = \frac{57}{13}
\]

So the solution to the system of equations is:

\[
\left(-\frac{9}{13}, \frac{57}{13}\right)
\]

In the response area, the solution is:

**(-9/13, 57/13)**