X+y =4 2x+3y=9

Question

Help? Systems.. 

Answer 1

Two ways we can approach this: Elimination or substitution. 

For Elimination, you want to get the coefficients of one of the variables the same in each equation - this may require multiplying one or both equations by a number. In this case, we can just multiply the first one by 2 to get
2x + 2y = 8
2x + 3y = 9

Now, subtract the second from the first, and we are left with 
-y = -1

Divide both sides by -1 to get y = 1. Now replace this back into one of the original equations to solve for x:

x + 1 = 4

x = 3

So our solution is (3,1)

For substitution, solve one of the equations for a variable, then substitute it into the other. Let's solve the first equation for x:
x = 4 - y

Now, substituting it into the second equation, we get
2(4 - y) + 3y = 9

8 - 2y + 3y = 9

8 + y = 9

y = 1

Putting this back into the first equation, we get x = 4 - 1 = 3