To solve the system of equations using substitution, we have:
- \( y = 5.8x + 15.24 \)
- \( y = -2x - 2.7 \)
Since both equations equal \( y \), we can set them equal to each other:
\[ 5.8x + 15.24 = -2x - 2.7 \]
Now, let's solve for \( x \):
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Add \( 2x \) to both sides: \[ 5.8x + 2x + 15.24 = -2.7 \] \[ 7.8x + 15.24 = -2.7 \]
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Subtract \( 15.24 \) from both sides: \[ 7.8x = -2.7 - 15.24 \] \[ 7.8x = -17.94 \]
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Now, divide by \( 7.8 \): \[ x = \frac{-17.94}{7.8} \approx -2.3 \]
Now that we have \( x \), substitute it back into one of the original equations to find \( y \). We will use the first equation:
\[ y = 5.8(-2.3) + 15.24 \] \[ y = -13.34 + 15.24 \] \[ y = 1.9 \]
Thus, the ordered pair solution where the two lines intersect is:
\[ \boxed{(-2.3, 1.9)} \]