To determine the solution of the given system of equations:
[tex]\[
\begin{array}{l}
5x - 4y = 6 \\
-5x + 4y = -10
\end{array}
\][/tex]
Let's follow a step-by-step approach:
1. Write down the system of linear equations:
[tex]\[
\begin{array}{l}
5x - 4y = 6 \quad \quad (1) \\
-5x + 4y = -10 \quad \quad (2)
\end{array}
\][/tex]
2. Add the equations to eliminate one of the variables:
By adding Equation (1) and Equation (2):
[tex]\[
(5x - 4y) + (-5x + 4y) = 6 + (-10)
\][/tex]
[tex]\[
0 = -4
\][/tex]
3. Analyze the result:
The resulting equation [tex]\(0 = -4\)[/tex] is a contradiction. This implies that the system of equations has no solution.
4. Conclusion:
Since the result we obtained is a contradiction, we conclude that the given system of equations has no solution.
This indicates that the lines represented by these equations are parallel and never intersect. Therefore, the correct answer is:
- no solution
