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 \( x \):
- Add \( x \) to both sides:
\[ 13x + x - 2 = 2 \]
This simplifies to:
\[ 14x - 2 = 2 \]
- Next, add \( 2 \) to both sides:
\[ 14x = 4 \]
- 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:
\[ \left( \frac{2}{7}, \frac{12}{7} \right) \]