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What is the solution to the system of equations?

[tex]\[
\begin{array}{l}
5x - 4y = 6 \\
-5x + 4y = -10
\end{array}
\][/tex]

A. [tex]\((4, 4)\)[/tex]
B. [tex]\((-2, -5)\)[/tex]
C. Infinitely many solutions
D. No solution


Sagot :

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