Question

y = -3/2x - 2 and 2x - y = -5

Answer 1

To solve the system of equations given by \( y = -\frac{3}{2}x - 2 \) and \( 2x - y = -5 \), we can use substitution or elimination. Here, I will use substitution.

We already have \( y \) expressed from the first equation:
\[
y = -\frac{3}{2}x - 2
\]

Now, we will substitute this expression for \( y \) into the second equation \( 2x - y = -5 \):
\[
2x - \left(-\frac{3}{2}x - 2\right) = -5
\]

This simplifies to:
\[
2x + \frac{3}{2}x + 2 = -5
\]

Next, combine the \( x \) terms:
\[
2x + \frac{3}{2}x = \frac{4}{2}x + \frac{3}{2}x = \frac{7}{2}x
\]

So we have:
\[
\frac{7}{2}x + 2 = -5
\]

Now, isolate the term with \( x \):
\[
\frac{7}{2}x = -5 - 2
\]
\[
\frac{7}{2}x = -7
\]

Now multiply both sides by \( \frac{2}{7} \):
\[
x = -7 \times \frac{2}{7} = -2
\]

Now that we have \( x \), we can substitute back to find \( y \):
\[
y = -\frac{3}{2}(-2) - 2
\]
\[
y = 3 - 2 = 1
\]

Therefore, the solution to the system of equations is:
\[
(x, y) = (-2, 1)
\]

To summarize, the solution is:
\[
\boxed{(-2, 1)}
\]