Question

Solve the following system using any method

X-y=-4

4x+3y=-9

Answer 1

To solve the system of equations:

1. \( x - y = -4 \)
2. \( 4x + 3y = -9 \)

We can use the substitution method.

First, let's express \( x \) in terms of \( y \) from the first equation:

\[
x = y - 4
\]

Now, we can substitute this expression for \( x \) into the second equation:

\[
4(y - 4) + 3y = -9
\]

Expanding this gives:

\[
4y - 16 + 3y = -9
\]

Combining like terms:

\[
7y - 16 = -9
\]

Next, we isolate \( y \):

\[
7y = -9 + 16
\]
\[
7y = 7
\]
\[
y = 1
\]

Now that we have \( y \), we can substitute back to find \( x \):

\[
x = y - 4
\]
\[
x = 1 - 4
\]
\[
x = -3
\]

The solution to the system of equations is:

\[
(x, y) = (-3, 1)
\]

You can check the solution by substituting both values back into the original equations:

1. For the first equation:
\[
-3 - 1 = -4 \quad (\text{True})
\]
2. For the second equation:
\[
4(-3) + 3(1) = -12 + 3 = -9 \quad (\text{True})
\]

So the final answer is:

\[
\boxed{(-3, 1)}
\]