To solve the given system of equations, we need to find the values of \( x \) and \( y \) that satisfy both equations simultaneously. The system of equations is:
[tex]\[
\begin{array}{r}
2x = 5y + 4 \\
3x - 2y = -16
\end{array}
\][/tex]
Let's follow a step-by-step process to solve this system.
### Step 1: Express one variable in terms of the other from the first equation.
From the first equation:
[tex]\[
2x = 5y + 4
\][/tex]
We can solve for \(x\):
[tex]\[
x = \frac{5y + 4}{2}
\][/tex]
### Step 2: Substitute this expression into the second equation.
Substitute \(x = \frac{5y + 4}{2}\) into the second equation, \(3x - 2y = -16\):
[tex]\[
3 \left( \frac{5y + 4}{2} \right) - 2y = -16
\][/tex]
### Step 3: Simplify the equation.
Multiply through by 2 to clear the fraction:
[tex]\[
3(5y + 4) - 4y = -32
\][/tex]
[tex]\[
15y + 12 - 4y = -32
\][/tex]
[tex]\[
11y + 12 = -32
\][/tex]
### Step 4: Solve for \(y\).
Isolate \(y\) by subtracting 12 from both sides:
[tex]\[
11y = -44
\][/tex]
Divide by 11:
[tex]\[
y = -4
\][/tex]
### Step 5: Substitute \(y = -4\) back into the expression for \(x\).
Now we use the expression \(x = \frac{5y + 4}{2}\):
[tex]\[
x = \frac{5(-4) + 4}{2}
\][/tex]
[tex]\[
x = \frac{-20 + 4}{2}
\][/tex]
[tex]\[
x = \frac{-16}{2}
\][/tex]
[tex]\[
x = -8
\][/tex]
### Final Solution:
The solution to the system of equations is \(x = -8\) and \(y = -4\).
Therefore, the correct answer choice is:
[tex]\[
(-8, -4)
\][/tex]
