Math help Algebra!?

Question

How would you solve this system using elimination?
x+y=3
x-y=1

Answer 1

I would add the two equations together, canceling out the "y" variable:

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

Now substitute the 2 back in for x in either equation:

2 + y = 3
y = 3 - 2
y = 1

Answer 2

First thing you want to do is pick a letter that you want to eliminate. It doesn't really matter which one you choose. You will learn, with practice, which one will be easier. Let's choose y. You need to make sure that the values of the y's in both equations are the same but opposite signs. In this case, it is already done. All you have to do now is add the two equations together.

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

Now that you know the value of x, pick one of the first equations and find the value of y by substituting x for 2.

Lets pick the first one
x+y = 3
2 + y = 3
y = 1

So this is your answer
x = 2 and y = 1

or you can write it as a point
(2, 1)

There you go :)

Answer 3

x + y = 3
x - y = 1 arranged to x = y + 1
x = y + 1 substituted into x + y = 3
y + 1 + y = 3
2y + 1 = 3
2y = 2 y = 1
substitute y = 1 into x + y = 3

x + 1 = 3 x = 2

x = 2 , y = 1

Answer 4

Add the 2 equations getting 2x = 4. so x=2, then substitue 2 back in getting y=1.

Answer 5

x + y = 3- - - - - - - Equation 1
x - y = 1- - - - - - - -Equation 2
- - - - - - -

2x = 4

2x / 2 = 4 / 2

x = 4 / 2

x = 2

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - - - - - -

x + y = 3

2 + y = 3

2 + y - 2 = 3 - 2

y = 1

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

x + y = 3

2 + 1 = 3

3 = 3

- - - - - - - -

Check for equation 2

x - y = 1

2 - 1 = 1

1 = 1

- - - - - - - -

Both equations balance

The solution set is { 2, 1 }

- - - - - - - - - - -s-

Answer 6

Add the two equations and you have:
x+y+x-y+ = 3+1
2x = 4
x=2

x+y=3
2+y=3
y=1

Answer 7

Add the equations:
2x = 4
x = 2
Subtract the equations (second from first):
2y = 2
y = 1

Answer 8

from the above
x=3-y

Substitute that into the second equation

(3-y)-y=1
3-2y=1
-2y=1-3
-2y=-2
y=1

Answer 9

just add the two equations together in the form that you have them, it is actually quite simple...
x+y=3
x-y=1
_______
2x=4

x=2

so if x equals 2, then y=1

Answer 10

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

x = 2

you add those lines together. + y and -y cancel out each other