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