To find the solution to the given system of equations:
[tex]\[
\begin{cases}
3x + 4y = -2 \\
2x - 4y = -8
\end{cases}
\][/tex]
we will solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
### Step 1: Write the equations
- The first equation is:
[tex]\[
3x + 4y = -2
\][/tex]
- The second equation is:
[tex]\[
2x - 4y = -8
\][/tex]
### Step 2: Add the equations to eliminate [tex]\( y \)[/tex]
If we add both equations together, we get:
[tex]\[
(3x + 4y) + (2x - 4y) = -2 + (-8)
\][/tex]
This simplifies to:
[tex]\[
3x + 2x + 4y - 4y = -10
\][/tex]
[tex]\[
5x = -10
\][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Divide by 5:
[tex]\[
x = \frac{-10}{5} = -2
\][/tex]
### Step 4: Substitute [tex]\( x \)[/tex] back into one of the original equations
Let’s use the first equation:
[tex]\[
3x + 4y = -2
\][/tex]
Substitute [tex]\( x = -2 \)[/tex]:
[tex]\[
3(-2) + 4y = -2
\][/tex]
This simplifies to:
[tex]\[
-6 + 4y = -2
\][/tex]
### Step 5: Solve for [tex]\( y \)[/tex]
Add 6 to both sides:
[tex]\[
4y = -2 + 6 = 4
\][/tex]
Divide by 4:
[tex]\[
y = \frac{4}{4} = 1
\][/tex]
### Final Answer
The solution of the system of equations is:
[tex]\[
x = -2 \quad \text{and} \quad y = 1
\][/tex]
Thus, the correct answer is:
(D) [tex]\( x = -2, y = 1 \)[/tex].
