To solve the system of equations given:
[tex]\[
\begin{array}{c}
4x + y = 16 \\
2x + 3y = -2
\end{array}
\][/tex]
we need to find the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations simultaneously.
### Step-by-Step Solution:
1. Label the equations for convenience:
[tex]\[
\text{(1) } 4x + y = 16
\][/tex]
[tex]\[
\text{(2) } 2x + 3y = -2
\][/tex]
2. Express [tex]\(y\)[/tex] from equation (1):
[tex]\[
y = 16 - 4x \tag{3}
\][/tex]
3. Substitute [tex]\(y\)[/tex] from equation (3) in equation (2):
[tex]\[
2x + 3(16 - 4x) = -2
\][/tex]
Simplify and solve for [tex]\(x\)[/tex]:
[tex]\[
2x + 48 - 12x = -2
\][/tex]
[tex]\[
2x - 12x = -2 - 48
\][/tex]
[tex]\[
-10x = -50
\][/tex]
[tex]\[
x = 5
\][/tex]
4. Substitute [tex]\(x = 5\)[/tex] back into equation (3) to find [tex]\(y\)[/tex]:
[tex]\[
y = 16 - 4 \times 5
\][/tex]
[tex]\[
y = 16 - 20
\][/tex]
[tex]\[
y = -4
\][/tex]
### Conclusion:
The solution to the system of equations is [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex]. Therefore, the correct answer is:
A. [tex]\((5, -4)\)[/tex].
