[tex] \left \{ {{x + 3y = 5} \atop {x - 3y = -1}} \right. [/tex]
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
---------------
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
