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The problem on the screen asks you to solve the system of equations using the method of elimination. The two given equations are:

1. \( 4x + 4y = 12 \)
2. \( 4x + 7y = 24 \)

### Steps for Elimination Method:

1. **Subtract the two equations** to eliminate \(x\):
   \[
   (4x + 7y) - (4x + 4y) = 24 - 12
   \]
   Simplifying:
   \[
   3y = 12
   \]

2. **Solve for \(y\)**:
   \[
   y = \frac{12}{3} = 4
   \]

3. **Substitute the value of \(y\) into one of the original equations** (say the first one):
   \[
   4x + 4(4) = 12
   \]
   Simplifying:
   \[
   4x + 16 = 12
   \]
   \[
   4x = 12 - 16
   \]
   \[
   4x = -4
   \]
   \[
   x = \frac{-4}{4} = -1
   \]

So, the solution to the system is \( x = -1 \) and \( y = 4 \).

You can now submit the answer \((-1, 4)\).

Would you like more details on any of the steps, or do you have any other questions?

### Related Questions:
1. How does the elimination method work for systems of equations?
2. Can elimination always be used, or are there situations where substitution is better?
3. What happens if the system of equations has no solution?
4. How can you solve systems of equations graphically?
5. What is the difference between consistent, inconsistent, and dependent systems of equations?

**Tip:** When using elimination, it's often easiest to eliminate the variable with the same coefficient across both equations.

Solve the system of equations using elimination: 4x + 4y = 12 and 4x + 7y = 24.

Learn how to solve the system of linear equations 4x + 4y = 12 and 4x + 7y = 24 using the elimination method. Follow a step-by-step solution covering key algebraic concepts, including solving for variables by elimination.

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