https://file.aiquickdraw.com/mathbot/file/1728624199027p25zgfsw.jpg

The system of equations provided is:

\[
\begin{aligned}
-4x + 4y &= 28 \\
-6x + 6y &= 43
\end{aligned}
\]

Let's solve this system by elimination or substitution.

### Step 1: Simplify the equations if possible
Notice both equations share common factors:

1st equation: 
\[
-4x + 4y = 28 \quad \text{can be simplified to} \quad -x + y = 7
\]

2nd equation: 
\[
-6x + 6y = 43 \quad \text{cannot be simplified easily}
\]

### Step 2: Eliminate one variable
We can multiply the first equation by 6 and the second by 4 to align the coefficients of \(x\):

\[
6(-x + y) = 6(7) \quad \Rightarrow \quad -6x + 6y = 42
\]
Now subtract this from the second equation:
\[
(-6x + 6y) - (-6x + 6y) = 43 - 42
\]
This simplifies to:
\[
0 = 1
\]

### Step 3: Analyze the result
The result \(0 = 1\) is a contradiction, meaning the system of equations has no solution. This happens when the lines represented by the equations are parallel and never intersect.

### Final Answer:
There is **no solution** for this system.

Would you like more details or have any questions?

Here are 5 related questions you might want to explore:
1. How do you identify if a system of equations is inconsistent?
2. What are the steps for solving systems of equations by substitution?
3. What is the geometric interpretation of parallel lines in a system of equations?
4. How can the determinant of a matrix help determine if a system has a solution?
5. What is the difference between consistent and inconsistent systems of equations?

**Tip:** Always check if simplifying the system at the start can make solving easier.

Solve the system of equations by Elimination/Addition:

-4x + 4y = 28
-6x + 6y = 43

This problem involves solving a system of linear equations using the Elimination method. The solution helps determine whether the system has one solution, no solution, or infinite solutions. Appropriate for students in Grades 9-12.

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