https://file.aiquickdraw.com/mathbot/file/172856917374101nn5ypz.jpg

The system of equations given in the image is:

\[
\begin{aligned}
1. & \quad 2x + 4y = 8 \\
2. & \quad 5x + 2y = -4
\end{aligned}
\]

We can solve this system of equations using the substitution method or elimination method. Let's use the elimination method here.

### Step 1: Multiply the equations to align coefficients

To eliminate \(y\), we can first make the coefficients of \(y\) the same by multiplying the equations by appropriate factors. Multiply the first equation by 1 (no change) and the second equation by 2:

\[
\begin{aligned}
1. & \quad 2x + 4y = 8 \quad \text{(Equation 1)} \\
2. & \quad 10x + 4y = -8 \quad \text{(Equation 2 multiplied by 2)}
\end{aligned}
\]

### Step 2: Subtract the equations

Now subtract Equation 1 from Equation 2 to eliminate \(y\):

\[
(10x + 4y) - (2x + 4y) = -8 - 8
\]

This simplifies to:

\[
8x = -16
\]

### Step 3: Solve for \(x\)

\[
x = \frac{-16}{8} = -2
\]

### Step 4: Substitute \(x = -2\) into one of the original equations

Now, substitute \(x = -2\) into the first equation to find \(y\):

\[
2(-2) + 4y = 8
\]

Simplifying:

\[
-4 + 4y = 8
\]

\[
4y = 12
\]

\[
y = \frac{12}{4} = 3
\]

### Solution:

The solution to the system of equations is \(x = -2\) and \(y = 3\). Therefore, the solution set is:

\[
(x, y) = (-2, 3)
\]

---

Do you have any questions or need further details on the steps? 

Here are 5 related questions to further explore this topic:
1. How would you solve this system using the substitution method?
2. What happens if two systems of equations have no solutions?
3. Can we graph these equations to confirm the solution?
4. How does the elimination method differ from the matrix method in solving systems?
5. What are some applications of solving systems of linear equations in real-life problems?

**Tip:** Always check your solution by substituting the values of \(x\) and \(y\) back into both original equations to verify correctness.

Himpunan penyelesaian sistem persamaan 2x + 4y = 8 dan 5x + 2y = -4 adalah . . .

Learn how to solve the system of linear equations 2x + 4y = 8 and 5x + 2y = -4 using the elimination method. This example involves aligning coefficients to eliminate variables and solving for both x and y. Suitable for high school students in Grades 10-12.

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