Given the system of equations, what is the solution? x + 3y = 5 x - 3y = -1

Immediately, you can tell that 3y and -3y will cancel out using elimination.  That would be the easiest solving method to use here.  Set up the problems like this, add them, and solve for the remaining variable:

x + 3y = 5
x - 3y = -1
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2x      = 4
x = 2

Now that you know what x is, you can substitute this value for x in one of the equations:

x + 3y = 5

2 + 3y = 5

3y = 3

y = 1

The solution to this system would be (2, 1).

You can perform a check for each equation to verify that this is the correct solution:

2 + 3(1) = 5

2 + 3 = 5

5 = 5
Correct

2 - 3(1) = -1

2 - 3 = -1

-1 = -1
Correct