What is the solution to this system of linear equations?

x + y = 4

x − y = 6

(4, 6)
(6, 4)
(5, −1)
(−1, 5)

Solve for one of the variables:
x+y=4
can be written as:
y=4 - x
If y=4 - x then we can substitute 4 - x in the second equation x-y=6

x - (4 - x)=6
Remember you have to distribute the negative sign in front of the parentheses to the numbers inside the parentheses.
x - 4 + x = 6
2x - 4 = 6
2x = 10
x=5
You can get the answer from this, but you can also figure out y. Just plug the x value back into the first equation.

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

Equation 1 ==> x + y = 4
Equation 2 ==> x - y = 6
Equation 3 ==> x = 6 + y

Substitude equation 3 into 1
6 + y + y = 4
2y = -2
y = -1

Substitude y into equation 2
x - (-1) = 6
x = 5

∴ Answer is C.