Answer: x=1/2 and y=4
Explanation:
There are two ways to go about this problem.
1. Substitution
2. Elimination
Substitution Method:
rearrange one of the equations so that it is in terms of a variable. I will rearrange the bottom equation which is 4x-y=-2 which can also be written as y=4x+2
Now we will plug that value of "y" into the first equation and get 2x + 3 *(4x+2)=13
Now we will solve for x
2x +12x+6=13
14x=7
x=7/14 or 1/2
Plug x into the the equation and solve for y
2(1/2) + 3y=13
3y=12
y=4
Check your answer by plugging both in to the second equation
4(1/2)-4=-2?
2-4=-2
-2=-2
Elimination Method:
In order to eliminate a term you need to have an x or y term that is equal or opposite so we can subtract or add both equations together. To do this we will multiple the top equation by a factor of 2 and end up with: 4x+6y=26
Now we are going to subtract the bottom equation from the top
4x+6y=26
-
4x-y=-2
7y=28
y=4
Plug in to get x
4x-4=-2
4x=2
x=2/4 or 1/2
Check!
2(1/2) + 3(4) = 13?
1+12=13
13=13