10. 4w - 2x + y -z = 3
2w +2x + y - z = 3
-w - 3x - 2y + z = 2
3w + 3x + 3y - 2z = 1
2w +2x + y - z = 3
-w - 3x - 2y + z = 2
3w + 3x + 3y - 2z = 1
-
4w - 2x + y - z = 3
2w + 2x + y - z = 3
_________________ -
2w - 4x = 0
w - 2x = 0
w = 2x ----------------------------------------…
4w - 2x + y - z = 3
-w - 3x - 2y + z = 2
_________________ +
3x - 5x - y = 5
3(2x) - 5x -y = 5
x - y = 5
y = 5 -x
-w - 3x - 2y + z = 2
3w + 3x + 3y - 2z = 1
__________________ +
2w + y - z = 3
2(2x) + (x - 5 ) - z = 3 ........... see above
4x + x - 5 -z = 3
5x - z = 8
z = 5x - 8
-w -3x - 2y + z = 2
-2x -3x - 2(x-5) + 5x - 8 = 2
-2x + 2 = 2
x = 0
y = x - 5 = 0 - 5 = -5
w = 2x = 0
z = 5x - 8 = -8
2w + 2x + y - z = 3
_________________ -
2w - 4x = 0
w - 2x = 0
w = 2x ----------------------------------------…
4w - 2x + y - z = 3
-w - 3x - 2y + z = 2
_________________ +
3x - 5x - y = 5
3(2x) - 5x -y = 5
x - y = 5
y = 5 -x
-w - 3x - 2y + z = 2
3w + 3x + 3y - 2z = 1
__________________ +
2w + y - z = 3
2(2x) + (x - 5 ) - z = 3 ........... see above
4x + x - 5 -z = 3
5x - z = 8
z = 5x - 8
-w -3x - 2y + z = 2
-2x -3x - 2(x-5) + 5x - 8 = 2
-2x + 2 = 2
x = 0
y = x - 5 = 0 - 5 = -5
w = 2x = 0
z = 5x - 8 = -8
-
4w - 2x + y -z = 3 .................................(A)
2w +2x + y - z = 3 .................................(B)
-w - 3x - 2y + z = 2 ................................(C)
3w + 3x + 3y - 2z = 1 ............................(D)
adding 2(C) to (B), 3(C) to (D) and 4(C) to (A) we get
-- 4x -- 3y + z = 7 ...................................(E)
-- 6x -- 3y + z = 7 ....................................(F)
-- 14x -- 7y + 3z = 11 .............................(G)
Subtracting (F) from (E), 2x = 0 OR x = 0 ANSWER
whence (E) gives z = 3y + 7 and (G) gives 3z = 11 + 7y which reduce to y = -- 5 and z = -- 8 ANSWER
Giving w = --3x -- 2y + z -- 2 = --2(--5) -- 8 -- 2 = 0 ANSWER
2w +2x + y - z = 3 .................................(B)
-w - 3x - 2y + z = 2 ................................(C)
3w + 3x + 3y - 2z = 1 ............................(D)
adding 2(C) to (B), 3(C) to (D) and 4(C) to (A) we get
-- 4x -- 3y + z = 7 ...................................(E)
-- 6x -- 3y + z = 7 ....................................(F)
-- 14x -- 7y + 3z = 11 .............................(G)
Subtracting (F) from (E), 2x = 0 OR x = 0 ANSWER
whence (E) gives z = 3y + 7 and (G) gives 3z = 11 + 7y which reduce to y = -- 5 and z = -- 8 ANSWER
Giving w = --3x -- 2y + z -- 2 = --2(--5) -- 8 -- 2 = 0 ANSWER