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To solve this system of linear equations:

\[
5x + 4y = 8
\]
\[
10x - 4y = 46
\]

we can use the elimination method. Here’s the step-by-step process:

### Step 1: Add the equations to eliminate \(y\)
The coefficients of \(y\) in both equations are \(+4y\) and \(-4y\). If we add the two equations, the \(y\) terms will cancel out:

\[
(5x + 4y) + (10x - 4y) = 8 + 46
\]

This simplifies to:

\[
15x = 54
\]

### Step 2: Solve for \(x\)
Divide both sides by 15:

\[
x = \frac{54}{15} = 3.6
\]

### Step 3: Substitute \(x\) back into one of the original equations
Let’s use the first equation:

\[
5x + 4y = 8
\]

Substitute \(x = 3.6\):

\[
5(3.6) + 4y = 8
\]
\[
18 + 4y = 8
\]

### Step 4: Solve for \(y\)
Subtract 18 from both sides:

\[
4y = 8 - 18
\]
\[
4y = -10
\]

Divide by 4:

\[
y = -2.5
\]

### Solution
The solution to the system is:
\[
x = 3.6, \, y = -2.5
\]

Would you like a more detailed explanation or have any questions?

### Here are 5 related questions:
1. How do you use the substitution method to solve a system of linear equations?
2. What happens if the system of equations has no solution or infinitely many solutions?
3. Can you explain how to graphically solve a system of equations?
4. What are some real-life applications of solving systems of equations?
5. How does the elimination method differ from the substitution method?

### Tip:
When using the elimination method, it's helpful to align terms neatly and double-check that you're properly adding or subtracting the equations to eliminate one variable.

Solve this system of linear equations without graphing: 5x + 4y = 8 and 10x - 4y = 46.

Explore how to solve the system of linear equations 5x + 4y = 8 and 10x - 4y = 46 using the elimination method. This step-by-step solution covers core concepts in algebra and is ideal for students in Grades 8-10.

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