Question

what is the solution of the system of equations?
2x+2y+3z=-1
4x+4y+3z=-5
4x+2y+2z=0

Answer 1

you want the long way or the short cut using matrices and a calculator

Answer 2

showing the work way, guess its long way

Answer 3

haha ok i recommend using a bunch of elimination to isolate a single variable

lets start by eliminating x:
pick 2 equations and eliminate x leaving an equation with y and z
4x +4y +3z = -5
-4x -2y -2z = 0 (I multiplied by -1 so x's would cancel)
---------------
2y +z = -5

Repeat with 2 other equations
-4x -4y-6z = 2 (I multiplied by -2 so x's would cancel)
4x +4y +3z =-5
---------------
-3z = -3 (just so happens y cancels as well, saves a step)
z = 1

substitute it into previous equation
2y + 1 = -5
y = -3

substitute both z,y values into one of original equation to get x
2x +2(-3) +3(1) = -1
2x -6 +3 = -1
x = 1

Solution: x=1,y=-3, z=1