<h3>
Answer: C. Infinite Solutions</h3>
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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 <em>exactly</em> 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 <u>infinitely many solutions</u>
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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 <u>infinitely many solutions</u>
Side note: The solutions are of the form (x,y) = (x,3x+4)
