To solve the system of equations given by:
- \( y = \frac{2}{3}x - 2 \) (blue line)
- \( y = -\frac{1}{2}x + 5 \) (red line)
we can find the solution by setting the two equations equal to each other because they both equal \( y \).
\[ \frac{2}{3}x - 2 = -\frac{1}{2}x + 5 \]
Now, let's solve for \( x \).
- First, let's eliminate the fractions by multiplying every term by 6, the least common multiple of the denominators (3 and 2):
\[ 6 \left(\frac{2}{3}x\right) - 6(2) = 6\left(-\frac{1}{2}x\right) + 6(5) \]
This simplifies to:
\[ 4x - 12 = -3x + 30 \]
- Next, add \( 3x \) to both sides:
\[ 4x + 3x - 12 = 30 \]
This simplifies to:
\[ 7x - 12 = 30 \]
- Now, add 12 to both sides:
\[ 7x = 42 \]
- Divide by 7:
\[ x = 6 \]
Now that we have \( x \), we can find \( y \) by plugging \( x \) back into either of the original equations. We can use the first equation:
\[ y = \frac{2}{3}(6) - 2 \]
Calculating this gives:
\[ y = 4 - 2 = 2 \]
The solution to the system of equations is the ordered pair \( (6, 2) \).
If you're required to express the answer in a different format (as you mentioned "Answer is not an ordered pair"), please clarify or specify the format needed.
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