Question

how do you substitute x+y=2 3x+2y=5

Answer 1

Here's how you solve this.  So, x+y=2, right?  Let's isolate x.  x+y-y=2-y.  x=2-y.  NOW, if x=2-y, in 3x+2y=5, we can REPLACE x with 2-y and use it to solve for y!  3x+2y=5.  3(2-y)+2y=5.  (3*2)+(3*-y)+2y=5.  6+(-3y)+2y=5.  6+(-y)=5.  6+(-y)-6=5-6.  -y=-1.  -y/-1=-1/-1.  y=1.

So, if y=1, we can substitute that back into either equation--but let's go with the easier one, x+y=2.  x+1=2.  x+1-1=2-1.  x=1.  1+1=2, so that works; let's check the other equation.  3(1)+2(1)=5.  3+2=5.  5=5.  That's correct!

Answer: x=1, y=1

Answer 2

First you have to solve for one of the unknowns in one of the problems, then substitute it into the other problem to solve for the other unknown... Sound complicated?... Not really! Let me show you...

Let's take the first equation... we'll solve for x

x + y = 2
x = 2 - y 

Ok, now we have an expression for the value of x.  It's 2 - y.  So let's substitute it into the other equation.

3x + 2y = 5
3 (2 - y) + 2y = 5  distribute the 3 into the parentheses
6 -3y + 2y = 5  now lets solve for y.  We need to isolate it so subtract 6                              from both sides.
6 - 3y + 2y - 6 = 5 - 6  Now combine like terms
-y = -1
y = 1

Now we have a number value for y we can substitute it back into the 1st equation and find the number value of x

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

So our answer is (1, 1)

Wasn't that easy!!