Solve the system by substitution.

{4x-6y=-20x=3y-8


We are given the system of equations:

\[
\begin{cases} 
4x - 6y = -20 \\
x = 3y - 8 
\end{cases}
\]

To solve this system by substitution, we'll follow these steps:

### Step 1: Substitute the expression for \(x\) from the second equation into the first equation.

The second equation is \(x = 3y - 8\). We'll substitute this into the first equation:

\[
4(3y - 8) - 6y = -20
\]

### Step 2: Simplify the equation.

Distribute the 4 on the left side:

\[
12y - 32 - 6y = -20
\]

Combine like terms:

\[
6y - 32 = -20
\]

### Step 3: Solve for \(y\).

Add 32 to both sides:

\[
6y = 12
\]

Now divide by 6:

\[
y = 2
\]

### Step 4: Substitute \(y = 2\) back into the second equation to solve for \(x\).

Use the equation \(x = 3y - 8\):

\[
x = 3(2) - 8 = 6 - 8 = -2
\]

### Final Solution:
The solution to the system is \(x = -2\) and \(y = 2\).

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

Would you like more details or have any other questions?

Here are 5 related questions to expand on this topic:

1. What are the advantages of solving a system by substitution compared to elimination?
2. How do you solve systems of equations graphically?
3. Can a system of equations have no solution or infinite solutions?
4. How would this problem change if the second equation were \(x = 3y + 8\)?
5. What methods can you use for solving systems of nonlinear equations?

**Tip:** Always double-check your substituted values by plugging them back into both original equations to verify they satisfy the system.

Solve the system by substitution: 4x - 6y = -20, x = 3y - 8

Learn how to solve the system of equations 4x - 6y = -20 and x = 3y - 8 by substitution. This step-by-step solution covers key algebra concepts and substitution techniques. Perfect for students in Grades 8-10.

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