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What is the solution to the system of equations below?
[tex]\[
\begin{array}{l}
3x + 4y = -2 \\
2x - 4y = -8
\end{array}
\][/tex]

A. [tex]\(x = 2, y = -2\)[/tex]

B. [tex]\(x = -2, y = 3\)[/tex]

C. [tex]\(x = 4, y = 4\)[/tex]

D. [tex]\(x = -2, y = 1\)[/tex]



Answer :

GinnyAnswer
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].

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