Question

Find the solution of the system of equations.
minus, 8, x, plus, 9, y, equals, minus, 21
−8x+9y=
−21
minus, 3, x, plus, 9, y, equals, minus, 36
−3x+9y=
−36

Answer 1

To solve the given system of equations:

1. \(-8x + 9y = -21\) (Equation 1)
2. \(-3x + 9y = -36\) (Equation 2)

We can start by isolating \(y\) in both equations or by elimination or substitution. Let's solve the system for \(y\).

First, we can simplify the system. Notice that both equations have \(9y\) on the left side. We can eliminate \(y\) by subtracting one equation from the other.

Let’s subtract Equation 2 from Equation 1:

\[
(-8x + 9y) - (-3x + 9y) = -21 - (-36)
\]

This simplifies to:

\[
-8x + 3x = -21 + 36
\]
\[
-5x = 15
\]

Now, solve for \(x\):

\[
x = \frac{15}{-5} = -3
\]

Now that we have \(x = -3\), we can substitute it back into either of the original equations to find \(y\). We can use Equation 1:

\[
-8(-3) + 9y = -21
\]

This becomes:

\[
24 + 9y = -21
\]

Now, isolate \(9y\):

\[
9y = -21 - 24
\]
\[
9y = -45
\]

Now, solve for \(y\):

\[
y = \frac{-45}{9} = -5
\]

Thus, the solution to the system of equations is:

\[
x = -3, \quad y = -5
\]

**Final Answer:**
\((x, y) = (-3, -5)\)