Answer
$(1,2,3,4)$
Work Step by Step
We multiply the second equation by two and add it to the third equation to find:
$3y+2z=12$
We multiply the first equation by 2 and add to the new equation above:
$4x+3y=10$
We now substitute $ x = 3-y$, which can be found using equation 4, to find:
$4(3-y)+3y=10$
$12-y=10$
$y=2$
We substitute $y=2$ into the last equation to find:
$x+2=3$
$x=1$
Now, we substitute x into the first equation to have:
$2(1)-z=-1$
$z=3$
Now, use the third equation and solve for z:
$ (2)-2w=-6$
We solve to find:
$w=4$
Thus, we have a solution:
$(1,2,3,4)$
