Solve \begin{cases} 3x-y=12 \\ 2x-y=8 \end{cases} by substitution.

To solve the system of equations

\[
\begin{cases} 
3x - y = 12 \\
2x - y = 8 
\end{cases}
\]

using substitution, let's proceed as follows:

### Step 1: Solve for \( y \) in terms of \( x \) from the first equation
Starting with:
\[
3x - y = 12
\]

Rearrange to isolate \( y \):
\[
y = 3x - 12
\]

### Step 2: Substitute \( y = 3x - 12 \) into the second equation
Now, substitute \( y \) from the first equation into the second equation:
\[
2x - (3x - 12) = 8
\]

### Step 3: Simplify and solve for \( x \)
Distribute and combine terms:
\[
2x - 3x + 12 = 8
\]
\[
-x + 12 = 8
\]

Subtract 12 from both sides:
\[
-x = -4
\]

Multiply both sides by \(-1\):
\[
x = 4
\]

### Step 4: Substitute \( x = 4 \) back into \( y = 3x - 12 \) to find \( y \)
Using \( y = 3x - 12 \):
\[
y = 3(4) - 12
\]
\[
y = 12 - 12
\]
\[
y = 0
\]

### Solution
The solution to the system is:
\[
(x, y) = (4, 0)
\]

Would you like additional details or have any questions?

### Related Questions
1. How would the solution change if we used the elimination method instead?
2. What if the system had no solutions? How would we determine that?
3. Can we solve this system by graphing? What would the graph look like?
4. What happens if we change one of the constants, say, in the second equation?
5. Could you set up a similar problem with slightly different values?

### Tip
When using substitution, always ensure your substitutions are correctly simplified to avoid calculation errors.

Solve \begin{cases} 3x-y=12 \\ 2x-y=8 \end{cases} by substitution.

Learn how to solve the system of linear equations 3x - y = 12 and 2x - y = 8 using the substitution method. This step-by-step guide covers algebraic techniques suitable for students in Grades 8-10.

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