Find the solution of the system of equations. $$ \begin{array}{c}-9 x-5 y=-18 \ 4 x+5 y=33\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
-9x - 5y = -18 \
4x + 5y = 33
\end{cases}
$$

**Step 1: Eliminate one variable**

Add the two equations to eliminate $$ y $$:

$$
(-9x - 5y) + (4x + 5y) = -18 + 33
$$

This simplifies to:

$$
-5x = 15
$$

**Step 2: Solve for $$ x $$**

$$
x = \frac{15}{-5} = -3
$$

**Step 3: Substitute $$ x $$ back into one of the original equations to find $$ y $$**

Using the second equation:

$$
4(-3) + 5y = 33
$$

$$
-12 + 5y = 33
$$

$$
5y = 45
$$

$$
y = 9
$$

**Solution:**

$$
(x, y) = (-3,\ 9)
$$
The solution to the system of equations is $$ x = -3 $$ and $$ y = 9 $$.

Find the solution of the system of equations. \[ \begin{array}{c}-9 x-5 y=-18 \\ 4 x+5 y=33\end{array} \]