Question

Find the solution of the system of equations.
8, x, minus, 6, y, equals, minus, 32
8x−6y=
−32
minus, 8, x, plus, 5, y, equals, 36
−8x+5y=
36

Answer 1

To solve the system of equations:

1. \( 8x - 6y = -32 \)
2. \( -8x + 5y = 36 \)

We can use the method of elimination or substitution. In this case, let's use elimination.

First, we can add both equations to eliminate \( x \):

\[
(8x - 6y) + (-8x + 5y) = -32 + 36
\]

This simplifies to:

\[
(-6y + 5y) = 4
\]

\[
-y = 4
\]

Now, multiplying both sides by -1, we get:

\[
y = -4
\]

Now that we have the value of \( y \), we can substitute it back into either of the original equations to solve for \( x \). Let's use the first equation:

\[
8x - 6(-4) = -32
\]

This simplifies to:

\[
8x + 24 = -32
\]

Now, subtracting 24 from both sides:

\[
8x = -32 - 24
\]

\[
8x = -56
\]

Now, divide by 8:

\[
x = -7
\]

So the solution to the system of equations is:

\[
x = -7, \quad y = -4
\]

Thus, the solution is:

\[
(x, y) = (-7, -4)
\]