The first step is to isolate one of the variables from one of the equations. We can pick either variable and either equation. The easiest to pick on is the 'x' from the first equation as the coefficient here is 1.
Isolate x in the first equation. Subtract 3y from both sides
x+3y = 8
x+3y-3y = 8-3y
x = 8-3y
So we can see that x is the same as 8-3y
Now move onto the second equation
3x - 5y = -18
3( x ) - 5y = -18 ... rewrite x so it has parenthesis around it
3( 8-3y) - 5y = -18 ... replace x with 8-3y; solve for y
24-9y - 5y = -18
24-14y = -18
24-14y-24 = -18-24
-14y = -42
-14y/(-14) = -42/(-14)
y = 3
If y = 3, then x is...
x = 8-3y
x = 8-3*3
x = 8-9
x = -1
The x and y values are x = -1 and y = 3
Together they pair up to form the ordered pair (x,y) = (-1,3)
The solution is (-1,3)
If you graph the two original lines, then they cross at (-1,3)
