https://file.aiquickdraw.com/mathbot/file/1727238382851vw0r9p93.jpg

The system of equations given in the image is:

1. \( 4x - 2y = 12 \)
2. \( -x + 5x - 2y = 0 \)
3. \( -9x + 4y = -8 \)

I will now solve this system step by step. Let me first simplify and solve the second equation.

The second equation simplifies as:
\[
-x + 5x - 2y = 0 \quad \Rightarrow \quad 4x - 2y = 0
\]

Now we have two equations:
\[
4x - 2y = 12 \quad \text{(Equation 1)}
\]
\[
4x - 2y = 0 \quad \text{(Simplified Equation 2)}
\]

We will start by solving these two equations first, then proceed to the third one. Let me handle that.The system of equations \( 4x - 2y = 12 \) and \( 4x - 2y = 0 \) results in no solution, as these are contradictory equations. They represent parallel lines, meaning they never intersect.

This suggests the system has no consistent solution. The equations are inconsistent, so no values of \( x \) and \( y \) satisfy both equations simultaneously.

Would you like to explore this further or have questions on this?

Here are 5 related questions you might want to explore:

1. How do parallel lines indicate no solution in a system of equations?
2. Can a system have infinitely many solutions, and how is that identified?
3. How can substitution or elimination methods help solve other systems of equations?
4. What are dependent and independent systems in terms of linear equations?
5. How can graphing be used to visualize the solution to a system of equations?

**Tip:** Always check if your system of equations is consistent (has solutions) or inconsistent (no solution) by analyzing their structure.

Solve the system of equations: 4x - 2y = 12, -x + 5x - 2y = 0, -9x + 4y = -8

Solve a system of linear equations involving the equations 4x - 2y = 12, -x + 5x - 2y = 0, and -9x + 4y = -8. This problem uses algebraic concepts, particularly the elimination method and inconsistency detection. Suitable for students in Grades 8-10.

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