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Let's solve this system of linear equations using substitution.

We are given two equations:
1. \(-5x + 3y = 51\)
2. \(y = 10x - 8\)

### Step 1: Substitute the second equation into the first.
Since \(y = 10x - 8\), we can substitute \(10x - 8\) for \(y\) in the first equation.

\[
-5x + 3(10x - 8) = 51
\]

### Step 2: Simplify the equation.
Expand the terms on the left-hand side:
\[
-5x + 30x - 24 = 51
\]

Combine like terms:
\[
25x - 24 = 51
\]

### Step 3: Solve for \(x\).
Add 24 to both sides:
\[
25x = 75
\]

Divide both sides by 25:
\[
x = 3
\]

### Step 4: Substitute \(x = 3\) into the second equation.
Now that we have \(x = 3\), substitute it into \(y = 10x - 8\) to find \(y\):
\[
y = 10(3) - 8 = 30 - 8 = 22
\]

### Final Solution:
The solution to the system of equations is \((x, y) = (3, 22)\).

Would you like further details or have any questions?

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Here are 5 related questions to expand on this concept:
1. How can you verify the solution to a system of linear equations?
2. What are the benefits of using substitution over other methods like elimination?
3. Can you apply the substitution method to nonlinear systems?
4. How would this method work if both equations were given in standard form?
5. What is the geometric interpretation of solving a system of linear equations?

**Tip:** Always substitute your solution back into the original equations to check for accuracy.

Solve the system of linear equations by substitution: -5x + 3y = 51, y = 10x - 8

Learn how to solve a system of linear equations using the substitution method. The example -5x + 3y = 51 and y = 10x - 8 demonstrates key algebraic concepts suitable for students in Grades 8-10.

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