Solve for x, y, and z: 5x - 2y = 19 , 3x + 3z = 21 , y + z = 2

Like when there are two unknowns, the best way to solve this kind of problem is to rearrange and substitute, but because there are three unknowns, it's a bit more fiddly. To solve this you want to pick and isolate one of the unknowns so you can find its value, and once you've done this the other two are easy. I'm picking x. Rearrange the first equation to make y the subject, to give y = (5x - 19)/2, and rearrange the second equation to make z the subject, giving z = 7 - x. This means you have both equations in terms of x.

Now, you can substitute these equations for y and z into y + z = 2, giving (5x - 19)/2 + 7 - x = 2. Because x is the only unknown, this can be simplified to give the value of x; it turns out that x = 3. Now this is known, x = 3 can be substituted into the other two original equations to find y and z, showing y = -2, and z = 4.