Solve the following system of equations by the elimination method.
4a
plus
nothingb
equals
28
nothinga
plus
4b
equals
minus8
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Part 1
What is the solution of the​ system? Select the correct choice​ below, and fill in the answer box if necessary.
A.
The solution is 
  
enter your response here.
​(Type an ordered pair. Use integers or fractions for any numbers in the​ expression.)
B.
There are infinitely many solutions.
C.
There is no solution.

To solve the given system of equations using the elimination method, we start by writing the system:

\[
4a + 0b = 28 \quad \text{(or just } 4a = 28\text{)}
\]
\[
0a + 4b = -8 \quad \text{(or just } 4b = -8\text{)}
\]

### Step 1: Solve for \( a \) and \( b \) individually
From the first equation \( 4a = 28 \), divide both sides by 4 to solve for \( a \):

\[
a = \frac{28}{4} = 7
\]

From the second equation \( 4b = -8 \), divide both sides by 4 to solve for \( b \):

\[
b = \frac{-8}{4} = -2
\]

### Step 2: Write the solution as an ordered pair
The solution to the system is:

\[
(a, b) = (7, -2)
\]

### Conclusion:
The correct choice is:

**A. The solution is \( (7, -2) \).**

Would you like further details or have any questions?

### Related Questions:
1. How does the elimination method work when both variables are present in both equations?
2. Can we solve this system by substitution instead? How would it compare?
3. What happens if the system had coefficients that resulted in a contradiction (e.g., no solution)?
4. How would the system look if it had infinitely many solutions?
5. How can we check if the solution \( (7, -2) \) is correct?

**Tip:** Always check your solution by substituting the values back into the original equations!

Solve the following system of equations by the elimination method. 4a + 0b = 28, 0a + 4b = -8. What is the solution of the system? Select the correct choice below: A. The solution is ( , ). B. There are infinitely many solutions. C. There is no solution.

Learn how to solve a system of linear equations using the elimination method. This problem involves solving 4a + 0b = 28 and 0a + 4b = -8 with step-by-step guidance, ideal for students in Grades 7-10.

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