Answer:
[tex]\left \{ {{-10x+y=4} \atop {10x-y=-4}} \right.[/tex]
Step-by-step explanation:
Which system of equations has infinitely many solutions?
4 x + 2 y = 5 // -4x - 2y = 1
-10x + y = 4 // 10x - y = -4.
-8x + y = 2 // 8x-y = 0.
-x + 2 y = 6 // 7x-2y = 12.
It's important to know that a linear system of equations has infinitely many solutions when both equations represents the same line, that means one line is on top of the other one, that's why the shared infinite points.
In this case, notice that if we compare the second system, you would find that both equations are the same,
[tex]\left \{ {{-10x+y=4} \atop {10x-y=-4}} \right.[/tex]
If we multiply the first equation by -1
[tex]\left \{ {{10x-y=-4} \atop {10x-y=-4}} \right.[/tex]
Which means the system has infinitely many solutions, because both equations represent the same line, so the shared all possibles points.
Therefore, the right answer is the second choice.
