To solve the system of equations:

1. \( x - 2y = 4 \)
2. \( x + y - 12 = 4 - 3y \)

we can proceed step-by-step:

### Step 1: Simplify the second equation

Starting with the second equation:

\[
x + y - 12 = 4 - 3y
\]

Simplify by adding \( 3y \) to both sides:

\[
x + 4y - 12 = 4
\]

Now, add 12 to both sides:

\[
x + 4y = 16
\]

So the simplified system of equations is:

1. \( x - 2y = 4 \)
2. \( x + 4y = 16 \)

### Step 2: Solve the system using elimination or substitution

Subtract the first equation from the second:

\[
(x + 4y) - (x - 2y) = 16 - 4
\]

Simplify:

\[
6y = 12
\]

Solve for \( y \):

\[
y = 2
\]

### Step 3: Find \( x \)

Substitute \( y = 2 \) into the first equation:

\[
x - 2(2) = 4
\]

\[
x - 4 = 4
\]

\[
x = 8
\]

### Solution

\[
(x, y) = (8, 2)
\]

Would you like further details or have any questions?

Here are five related questions you might find helpful:
1. How do you solve systems of equations using substitution?
2. Can you solve a system of equations graphically?
3. What are some other methods to solve linear systems besides elimination?
4. How do you check if a solution is correct in a system of equations?
5. How do you deal with systems that have no solution or infinitely many solutions?

**Tip:** Always check your solution by substituting back into the original equations to ensure they are satisfied!

x - 2y = 4; x + y - 12 = 4 - 3y. Solve for (x, y).

Learn how to solve the system of linear equations x - 2y = 4 and x + y - 12 = 4 - 3y using the elimination method. This step-by-step solution covers key algebraic concepts, including simplification, elimination, and substitution. Ideal for students in Grades 9-10.

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