w+x+y+z=2

Question

2w-x-y+2z=7
2w+3x+2y-z=-2
3w-2x-y-3z=-2
solve for w, x, y, z

Answer 1

No.
Eliminate variables one at a time, or use Kramer's method of determinants.

Here is how to get rid of x. Add the first two equations.

3w + 3z = 9 or
w + z = 3

Multiply the third equation by 2 and the fourth equation by 3, and add.
4w + 6x + 4y - 2z = -4
9w - 6x - 3y - 9z = -6
13w -y - 11z = -10

Continue in that manner until you are left with the value of one of the variables.