What is x+y=13 x-y=5 solve for the systems of equation in Algebra 1

i am doing algebra 1 and I'm solving for the systems of equations the equation is x+y=13
x-y=5

What is x+y=13 x-y=5 solve for the systems of equation in Algebra 1?
i am doing algebra 1 and I'm solving for the systems of equations the equation is x+y=13 x-y=5

first add both equation
x+y=13
x-y=5

you will end up with (y-y will cancel each other) then we will have:
2x =18

Let divide both side by 2 because we want to have x by itself
2x/2 = 18/2

The new will end up with:
X=9

Then go back in the first equation and substitute the value of x
9+y=13(subtract both side by 8 then we will have)
y = 4

Then go back to second equation and substitute the value of x as well
9-y = 5 (subtract both sides by -9 and you will end up with:
-y = -4 (then divide both side by -1) then you will end with:
Y=4


Result: X=9
y = 4

Now plug in each value in each equation to verify the answer
x+y=13-----------9+4=13
x-y=5--------------9-4=5

I worked out all the steps and explained to you everything that I did so that you can understand. It was not difficult after all. If you keep practicing by following all the steps provided in the problem, pretty soon you will find yourself in front of a classroom and explain to your classmates how to work similar problem in heart beat. Good luck!

x+y = 13
x-y = 5

Solving for y:

-1(x+y) = (-1)13 :: Multiply both sides (of the top equation) by -1

-x - y = -13
x - y = 5

-2y = -8 :: The X's cancel out and -13 + 5 = -8
y = 4 :: divide both sides by -2

--------------------
Solving for X:

x + y = 13
x - y = 5

2x = 18 :: The Y's cancel out and 13 + 5 = 18