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!