Question 254127: Please solve for w, x, y, and z.
1. x + 3w = 4
2y - z -w = 0
3y - 2w = 1
2x - y + 4z =5
2. x + y + z + w = 6
2x + 3y - w = 0
-3x + 4y + z + 2w = 4
x + 2y -z +w = 0
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! Please solve for w, x, y, and z.
1. x + 3w = 4
2y - z -w = 0
3y - 2w = 1
2x - y + 4z =5
x+3w=4
x=-3w+4
3w=4-x
w=(4/3)-(1/3)x
2y-z-w=0
2y-z-(4/3)+(1/3)x=0
(1/3)x+2y-z=4/3
x+6y-3z=4
3y-2w=1
-2w=1-3y
w=-(1/2)+(3/2)y
x+3W=4
x-(3/2)+(9/2)y=4
2x-3+9y=8
2x+9y=11
3y-2w=1
3y-(8/3)+(2/3)x=1
9y-8+2x=3
2x+9y=11
2x+9y=11
x+6y-3z=4 * -2
2x-y+4z=5
2x+9y=11
-2x-12y+6z=-8 + 1st
2x-y+4z=5
2x+9y =11
-3y+6z = 3 * -1/3
2x-y +4z = 5
2x+9y =11
y -2z =-1 *2
2x-y+4z =5
2x+9y =11
2y -4z =-2
2x-y+4z =5 + 2nd
2x+9y =11
2y -4z =-2
2x+y =3
2x+9y-11=2x+y-3
8y=-3+11
8y=8
y=1
2x+9y=11
2x+9=11
2x=2
x=1
x+3w=4
1+3w=4
w=1
2y - z -w = 0
2-z-1=0
1-z=0
z=1
2. x + y + z + w = 6
2x + 3y - w = 0
-3x + 4y + z + 2w = 4
x + 2y -z +w = 0
w=6-x-y-z
2x+3y-6+x+y+z=0 --> 3x+4y+z=6
-3x+4y+z+12-2x-2y-2z=4 --> -5x+2y-z=-8 add 1st
x+2y-z+6-x-y-z=0 --> y-2z=-6
3x +4y+z =6 *2
-2x+6y =-2
y-2z=-6
6x+8y+2z=12 add 3rd
-2x+6y =-2
y-2z=-6
6x+8y =6
-2x+6y =-2 *3
y-2z=-6
6x+8y = 6
-6x+18y =-6 add 1st
y-2z=-6
6x+8y = 6
26y = 0
y-2z=-6
y=0
-2z=-6
z=3
6x+8y=6
6x=6
x=1
w=6-x-y-z
w=6-1-0-3
w=2
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