The concept of solving a problem by elimination is to solve for one variable, by getting rid of the other.
Let's solve [2y = x + 2, x - 3y = -5] in terms of y.
Start by transforming the second equation into one of the same form as the first (y = x + c).
x-3y = -5
x = -5 + 3y
3y = x+5
Now we have two equations that are in the same form:
3y = x+5
2y = x+2
To solve in terms of y, we need to get rid of x -- so subtract the first equation from the second equation - this will yield the following:
y = 3 [[ 3y - 2y = y, x - x = 0, 5 - 2 = 3 ]]
Now take this information and solve for x:
2(3) = x+2
6 = x+2
x = 4
Now we have the solution, just make it a coordinate point:
(4, 3)
