Certainly! Let's solve the system of linear equations step by step. We are given the following two equations:
1. [tex]\(5x - 2y = 6\)[/tex]
2. [tex]\(5x - 2y = -4\)[/tex]
### Step 1: Analyze the Equations
Look closely at the two equations. We observe that the left-hand side (LHS) of both equations is identical, but the right-hand side (RHS) is different. This tells us that:
- [tex]\(5x - 2y\)[/tex] is equal to 6 (from the first equation), and
- [tex]\(5x - 2y\)[/tex] is also equal to -4 (from the second equation).
### Step 2: Identify Contradiction
For [tex]\(5x - 2y\)[/tex] to be simultaneously equal to both 6 and -4 is impossible. This contradicts the fundamental property of equality. Therefore, no value of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] can satisfy these conditions at the same time.
### Conclusion
Given the contradiction within these equations, there is no solution to this system of equations. The system is inconsistent.
That is, there are no values for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that will satisfy both equations simultaneously. Therefore:
[tex]\[
\boxed{\text{No solution}}
\][/tex]
