To solve the system of equations, we need to find the point where the two lines intersect. The first equation is:
- \( y = \frac{1}{3}x + 2 \)
The second equation appears to be incorrectly written. It likely should be of the form \( y = \frac{4}{3}x - 5 \) if we assume you meant it should be a linear equation.
Let's assume the second equation is:
- \( y = \frac{4}{3}x - 5 \)
To find the solution, we will set these two equations equal to each other:
\[ \frac{1}{3}x + 2 = \frac{4}{3}x - 5 \]
Now we can solve for \( x \).
- Multiply the entire equation by 3 to eliminate fractions:
\[ x + 6 = 4x - 15 \]
- Rearranging gives:
\[ 6 + 15 = 4x - x \]
\[ 21 = 3x \]
- Divide by 3:
\[ x = 7 \]
Now that we have \( x = 7 \), we will substitute this value back into either equation to find \( y \). Using the first equation:
\[ y = \frac{1}{3}(7) + 2 = \frac{7}{3} + 2 = \frac{7}{3} + \frac{6}{3} = \frac{13}{3} \]
Therefore, the solution to the system of equations is:
\[ (x, y) = (7, \frac{13}{3}) \]
Thus, the answer is:
(7, \( \frac{13}{3} \))
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