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The question appears to involve solving a system of linear equations using the elimination method. To solve this, let me first interpret the equations provided in the image.

The image shows the following system of equations:

\[
\frac{2}{3}x + \frac{5}{3}y = 4
\]
\[
2x + y = 4
\]

Let's solve this system using the elimination method:

### Step 1: Clear the fractions in the first equation
Multiply the entire first equation by 3 to eliminate the fractions:

\[
3 \times \left(\frac{2}{3}x + \frac{5}{3}y = 4\right)
\]

This simplifies to:

\[
2x + 5y = 12
\]

Now we have the following system of equations:

\[
2x + 5y = 12 \quad \text{(Equation 1)}
\]
\[
2x + y = 4 \quad \text{(Equation 2)}
\]

### Step 2: Eliminate one variable
To eliminate \(x\), subtract Equation 2 from Equation 1:

\[
(2x + 5y) - (2x + y) = 12 - 4
\]

This simplifies to:

\[
4y = 8
\]

### Step 3: Solve for \(y\)
Divide both sides by 4:

\[
y = 2
\]

### Step 4: Substitute \(y = 2\) back into one of the original equations to find \(x\)
Substitute \(y = 2\) into Equation 2:

\[
2x + 2 = 4
\]

Subtract 2 from both sides:

\[
2x = 2
\]

Divide by 2:

\[
x = 1
\]

### Solution
The solution to the system of equations is \(x = 1\) and \(y = 2\).

Would you like more details or have any questions about this solution?

Here are five questions related to the problem:

1. What would be the solution if we used substitution instead of elimination?
2. How do we handle systems of equations when both variables are eliminated?
3. What are the advantages of using elimination over substitution?
4. How do we solve systems of linear equations with more than two variables?
5. What does the solution \(x = 1\) and \(y = 2\) represent graphically?

**Tip:** Always double-check your solution by substituting the values back into the original equations to ensure accuracy.

Learn how to solve a system of linear equations using the elimination method with step-by-step instructions. This problem involves solving two equations with two variables, demonstrating key concepts in algebra and linear equations.

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