What is the solution to the system of equations?
2x-3y-z=-6,
4x-y-z=-2
-x+2y-2z=-9

x=7/13, y=19/13, z=74/13

Step-by-step explanation:

Add or subtract multiples of equations to eliminate one variable. I picked z to eliminate.

Subtract the 1st equation from the 2nd equation.

2x + 2Y = 4 or x + y = 2 or y = -x + 2, then

Multiple the 2nd equation by 2 and subtract the 3rd equation.

9x - 4y = 5 then sub (-x + 2) for y from previous step.

9x - 4(-x +2) = 5

13x -2 = 5

13x = 7

x = 7/13

plug that into either of the step 1 equations to gey y.

y = -x + 2

y = -7/13 + 2

y = 19/13

then plug the found x and y into any one of the original equations to get z.

-x + 2y - 2z = -9

-7/13 + 2(19/13) - 2z = -9

31/13 - 2z = -9

-2z = -9 - 31/13

-2z = -117/13 - 31/13 = -148/13

z = 74/13