Question

Solve the system of equations. −6x + 2y = −32 and 4 x + 3y = −9

Answer 1

To solve the system of equations:

1. \(-6x + 2y = -32\) (Equation 1)
2. \(4x + 3y = -9\) (Equation 2)

Let's first simplify Equation 1 by dividing everything by 2:

\[
-3x + y = -16
\]

Now we can express \(y\) in terms of \(x\):

\[
y = 3x - 16
\]

Next, we can substitute \(y\) from Equation 1 into Equation 2:

\[
4x + 3(3x - 16) = -9
\]

Expanding this equation:

\[
4x + 9x - 48 = -9
\]

Combining like terms gives us:

\[
13x - 48 = -9
\]

Now, add 48 to both sides:

\[
13x = 39
\]

Now, divide by 13:

\[
x = 3
\]

Now that we have \(x\), we can substitute it back into the equation for \(y\):

\[
y = 3(3) - 16
\]
\[
y = 9 - 16
\]
\[
y = -7
\]

Thus, the solution to the system of equations is:

\[
x = 3, \quad y = -7
\]

The solution is \((3, -7)\).