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 can set them equal to each other:

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

Now, let's solve for \( x \):

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

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

This simplifies to:

\[
14x - 2 = 2
\]

2. Add 2 to both sides:

\[
14x = 4
\]

3. Divide by 14:

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

Now, plug \( x = \frac{2}{7} \) back into one of the original equations to find \( y \). We'll use the second equation \( y = -x + 2 \):

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

To combine these, 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 system of equations is:

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

So the final answer is:

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