Question

The system of equations y=−15x−6
and y=−2x+3
is shown on the graph below.



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

NOTE: In the bottom right corner of each question, you will see an option to check answer. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.

Answer 1

To find the solution to the system of equations given by \(y = -15x - 6\) and \(y = -2x + 3\), we need to identify the point where the two lines intersect.

This can be done by setting the two equations equal to each other:

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

To solve this equation, first, we'll move all terms involving \(x\) to one side:

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

This simplifies to:

\[
-13x = 9
\]

Now, divide both sides by -13:

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

Next, we need to find the corresponding value of \(y\). We can substitute \(x = -\frac{9}{13}\) into either of the original equations. Let's use \(y = -2x + 3\):

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

This simplifies to:

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

Thus, the solution to the system of equations is:

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

So, you would input \((-9/13, 57/13)\) into the response areas. Make sure to check your answer as prompted.