solve x+2y-z=12,3/2x+2/3y-1/2z=-7,1/4x+2/3y-1/2z=1

Question: solve x+2y-z=12,3/2x+2/3y-1/2z=-7,1/4x+2/3y-1/2z=1.

The three simultaneous equations are,

x+2y-z=12  ------------------------------- (1)
3/2x+2/3y-1/2z=-7   -------------------- (2)
1/4x+2/3y-1/2z=1    -------------------- (3)

Multiply (2) by 6, and (3) by12 to get rid of fractions.

x + 2y - z = 12  ------------------------- (4)
9x + 4y - 3z = -42   -------------------- (5)
3x + 8y - 6z = 12    -------------------- (6)

Substitute x = 12 - 2y + z, from (4), into (5) and (6).

9(12 - 2y + z) + 4y - 3z = -42   -------------------- (5)
3(12 - 2y + z) + 8y - 6z = 12    -------------------- (6)

These equations simplify to

-14y + 6z = -150   ----------------------------------- (7)
2y - 3z = -24     --------------------------------------- (8)

-10y = -198

y = 99/5

Substitute for y = 99/5 into (8).

198/5 - 3z = -24

66/5 - z = -8

z = 66/5 + 8 = (66+40)/5 = 106/5

z = 1065/5

Substitute for y = 99/5 and z = 106/5 into (1).

x + 198/5 - 106/5 = 12

x + 92/5 = 12

x = 12 - 92/5 = (60 - 92)/5 = -32/5

x = -32/5

Answer: x = -32/5, y = 99/5, z = 106/5

by Level 11 User (81.5k points)