Question

How do you solve substitution to solve the sytem x+y=2 -2x+y=2

Answer 1

So you want to make one of the equations equal to one of the placeholders exg y=x+3

so we have
x+y=2 and
-2x+y=2

I chose to make -2x+y=2 equal to y so
-2x+y=2
add 2x to both sides
y=2+2x

subsitute 2+2x for y in x+y=2
x+2+2x=2
add like terms
3x+2=2
subtract 2 from both sides
3x=0
x=0

subsitute x=0 in x+y=2
0+y=2
y=2

x=0
y=2

Answer 2

Separate one variable in either equation, so for example:

x=-y+2
-2x+y=2 

 (if you dont know how to do that, tell me)

now that you have the variable separated, you can substitute the top equation in for the x in the second equation like this

-2(-y+2)+y=2

and now use the distributive property to get:

2y-4+y=2

and just combine like numbers.....

3y-4=2

and if you dont know how to solve it from here, comment to tell me but the rest of the problem would go like this:

3y-4=2
   +4 +4

3y=6
 /3  /3

y=2

and then you take this y and plug it back into one of the original two equations waaayy up at the top like this:

x+2=2

and solve...

x+2=2
  -2 -2 

x=0

so your final answer is (0,2)! Hope this helps!