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Explanation:

The two equations almost look eerily identical. The only difference really is that the second equation has minus signs littered throughout.

So a good (and correct) guess would be to multiply everything in the second equation by -1 to get...

-y = -3x-4

-1*(-y) = -1*(-3x-4)

y = 3x+4

We get exactly the same result as the first equation in the original given system of equations.

Since we have two identical lines, they will intersect infinitely many times.

Therefore, this system has infinitely many solutions

Here's another viewpoint.

Since  y = 3x+4, as shown in the first original equation, we can replace the 'y' in the second equation with 3x+4 and solve for x

-y = -3x-4

-1y = -3x-4

-1(3x+4) = -3x-4

-3x-4 = -3x-4

At this point, we can see the same thing is on both sides. That equation will ultimately simplify to 0 = 0 when we add 3x to both sides, and when we add 4 to both sides.

Getting 0 = 0 as a final result means there are infinitely many solutions

Side note: The solutions are of the form (x,y) = (x,3x+4)

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