ANSWER and EXPLANATION
We want to solve the system of equations given:
[tex]\begin{gathered} -5x+7y=8 \\ 5x-7y=-8 \end{gathered}[/tex]
Let us solve it by adding the equations:
[tex]\begin{gathered} -5x+7y+5x-7y=8+(-8) \\ -5x+5x+7y-7y=8-8 \\ \Rightarrow0+0=0 \\ \Rightarrow0=0 \end{gathered}[/tex]
The above statement is true.
As we can see above, 0 appears on both sides of the solution.
This implies that the system of equations has infinitely many solutions.
