Question

The graph shows the equation y=13x−2
in red and the equation y=−x+2
in blue.





(2 points)
What ordered pair is the solution of these two equations?

(
,
)

Answer 1

To find the solution of the two equations \( y = 13x - 2 \) and \( y = -x + 2 \), we need to find the point where the two lines intersect. This means we can set the two equations equal to each other:

\[
13x - 2 = -x + 2
\]

Now, solve for \( x \):

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

\[
13x + x - 2 = 2
\]

This simplifies to:

\[
14x - 2 = 2
\]

2. Next, add \( 2 \) to both sides:

\[
14x = 4
\]

3. Now, divide by \( 14 \):

\[
x = \frac{4}{14} = \frac{2}{7}
\]

Now that we have the value of \( x \), we can substitute it back into either equation to find the corresponding \( y \). Let's use \( y = -x + 2 \):

\[
y = -\frac{2}{7} + 2
\]

Convert \( 2 \) to a fraction:

\[
y = -\frac{2}{7} + \frac{14}{7} = \frac{12}{7}
\]

Thus, the ordered pair that is the solution to the two equations is:

\[
\left( \frac{2}{7}, \frac{12}{7} \right)
\]

So, the answer is:

\[
\left( \frac{2}{7}, \frac{12}{7} \right)
\]