Question

Is (3,4) a solution to the system of equations. X + y = 7 x - 2y = - 5

Answer 1

Answer: Yes, the point (3,4) is a solution to the system.

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Proof of this:

Replace x with 3 and y with 4 in the first equation

x+y = 7

3+4 = 7

7 = 7

This confirms the first equation. Repeat for the second equation

x-2y = -5

3-2(4) = -5

3 - 8 = -5

-5 = -5

We get true equations for both when we plug in (x,y) = (3,4). This confirms it is a valid solution to the system of equations. It turns out it's the only solution to this system of equations. Visually, the two lines cross at the single location (3,4).