To find the y-coordinate of the solution to the system of equations given, we can use either substitution or elimination. In this case, let's use substitution.
The first equation is:
\[ y = -3x + 2 \]
We can substitute this expression for \( y \) into the second equation:
\[ 5x + 3(-3x + 2) = 0 \]
Now simplify the equation:
\[ 5x - 9x + 6 = 0 \] \[ -4x + 6 = 0 \]
Next, solve for \( x \):
\[ -4x = -6 \] \[ x = \frac{-6}{-4} = \frac{3}{2} \]
Now that we have the value of \( x \), we can substitute it back into the first equation to find \( y \):
\[ y = -3\left(\frac{3}{2}\right) + 2 \] \[ y = -\frac{9}{2} + 2 \] \[ y = -\frac{9}{2} + \frac{4}{2} \] \[ y = -\frac{5}{2} \]
Thus, the y-coordinate of the solution to the system of equations is:
\[ \boxed{-\frac{5}{2}} \]
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