Question 442408
I am going to do this using substitution and then by elimination.

SUBSTITUTION METHOD
Let's solve the first one in terms of y.

y = 3-x.

Plug 3-x where you see y in the second equation.

2x - 3(3-x) = 16

2x - 9 +3x = 16

5x -9 = 16

5x = 25

x = 5

Plug x=5 back into the other equation.

2(5) - 3y = 16

10 - 3y = 16

-3y = 6

y = -2

So our solution is (5,-2)  or {{{x=5}}}{{{y=-2}}}


ELIMINATION METHOD
x+y =3
2x-3y=16

I'm going to eliminate the y.

Multiply the top equation by 3.

3(x+y = 3)
2x-3y = 16
-------------Simplify
3x+3y=9
2x-3y=16

Add the two equations together.

5x + 0y = 25

x = 5

Then substitute x=5 back into one of the original equations, let's use the first.

5 + y = 3

y = -2

So your solution is  (5,-2)  or  {{{x=5}}}{{{y=-2}}}

Hope this helped!