Question

\begin{aligned}
y&=-4x -5
\\\\
y&=3x -2
\end{aligned}

Answer 1

To solve the system of equations given by:

\[
y = -4x - 5
\]

\[
y = 3x - 2
\]

we can set the two equations equal to each other since both expressions equal \( y \):

\[
-4x - 5 = 3x - 2
\]

Now, we'll solve for \( x \).

1. Add \( 4x \) to both sides:

\[
-5 = 3x + 4x - 2
\]

This simplifies to:

\[
-5 = 7x - 2
\]

2. Now add \( 2 \) to both sides:

\[
-5 + 2 = 7x
\]

This simplifies to:

\[
-3 = 7x
\]

3. Now, divide both sides by \( 7 \):

\[
x = -\frac{3}{7}
\]

Now that we have the value of \( x \), we can substitute it back into either of the original equations to find \( y \). We'll use the second equation \( y = 3x - 2 \):

\[
y = 3\left(-\frac{3}{7}\right) - 2
\]

Calculating that gives:

\[
y = -\frac{9}{7} - 2
\]

To combine the terms, notice that \( 2 \) can be written as \( \frac{14}{7} \):

\[
y = -\frac{9}{7} - \frac{14}{7} = -\frac{23}{7}
\]

Thus, the solution to the system of equations is:

\[
\left( x, y \right) = \left( -\frac{3}{7}, -\frac{23}{7} \right)
\]

So, the final answer is:

\[
\boxed{\left( -\frac{3}{7}, -\frac{23}{7} \right)}
\]