okay i am having trouble on this please help?

Question

it is using elimination using addition and subtraction

x-y=1
x+y=3

so the ys cancel out making it 2x=4 then divide both sides by 2 and x=2 now i have to plug it into the next equasion and thats where i need help i you could please do it step by step like above thanks guys!

Answer 1

The REASON the y's cancel is because you are adding the two equations...

x - y = 1
x + y = 3
______ now add them

(x+x) (-y+y) = (1+3)
2x + 0 = 4
2x = 4
divide by 2
x = 2

now you plug the 2 in for x in one of the equations

x-y=1
(plug in the 2 for x)
2-y=1
(solve for y now...)
(add y to both sides)
2 = 1+y
(subtract 1 from both sides)
1 = y

You could have substituted into the other equation too...
x+y=3
(substitute 2 for x)
2+y=3
(subtract 2 from both sides)
y = 1

so x = 2 and y = 1 and you have the point (2,1) where the graphs of the two equations meet...I'll show you...

put both of the equations into slope-intercept form (or just get y onto one side by itself)
x-y = 1
(add y to both sides)
x=y+1
(subtract 1 from both sides)
y = x - 1

Now do the other equation...
x+y=3
(subtract x from both sides)
y = 3-x

Now plot both lines, y = x-1 and y = 3-x and you will see that they cross at the point (x,y) of (2,1).. which is the only location where x-y=1 AND x+y=3

Answer 2

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

2x / 2 = 4 / 2

x = 4 / 2

x = 2

Insert the x value into equation 1

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

x - y = 1

2 - y = 1

2 - y - 2 = 1 - 2

- y = - 1

Multiply the equation - y = - 1 by - 1 to make y positive.

- 1(- y) = - 1(- 1

y = 1

Insert the y value into equation 1

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

Check for equation 1

x - y = 1

2 - 1 = 1

1 = 1

- - - - - -

Check for equation 2

x + y = 3

2 + 1 = 3

3 = 3

- - - - - - - - -

The two equations balance

The solution set is { 2, 1 }

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

Answer 3

Now you have:
x=2
x-y=1

So subtract the 2nd from the first. The x's cancel out and you have -(-y)=1, which means y=1.
-------------------------------------------------------------
Or, you could have used the last equation:
x=2
x+y=3
This time, subtract the 1st equation from the 2nd. The x's drop out and you are left with y=3-2, so y=1.

Answer 4

Replace x with 2 in one (or both) equations:

2 - y = 1
y = 1

or...
2 + y = 3
y = 1

Good luck!

Answer 5

Plug it into one of them: write '2' instead of 'x'

2-y=1 // -1

1-y = 0 // + y

1 = y or y = 1

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

2 + y = 3 // -2

y = 1