SOLUTION: Please help! I am so confused! 3. Solve for X, Y, and Z in the following systems of three equations: a. X + 2Y + Z = 6 X + Y = 4 3X + Y + Z = 8 b. 10X + Y

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Please help! I am so confused! 3. Solve for X, Y, and Z in the following systems of three equations: a. X + 2Y + Z = 6 X + Y = 4 3X + Y + Z = 8 b. 10X + Y      Log On


   

Question 167664: Please help! I am so confused!
3. Solve for X, Y, and Z in the following systems of three equations:
a. X + 2Y + Z = 6
X + Y = 4
3X + Y + Z = 8
b. 10X + Y + Z = 12
8X + 2Y +Z = 11
20X - 10Y - 2Z = 8
c. 22X + 5Y + 7Z = 12
10X + 3Y + 2Z = 5
9X + 2Y + 12Z = 14
Answer by rviksub(2) About Me  (Show Source):
You can put this solution on YOUR website!
a.
X + 2Y + Z = 6 …………. Equation 1
X + Y = 4 ……………….. Equation 2
3X + Y + Z = 8………….. Equation 3
From Eqn 2, X= 4-Y
Substitute this value of X in Eqn 1 and Eqn 1 becomes
(4-Y)+2Y+Z=6
» 4+Y+Z=6 i.e., Y+Z=2….Eqn 4
Substitute the value of Y+Z in Eqn 4 in Eqn 3
3X+2=8 » 3X=6 » X=2
Substitute X=2 in Eqn 2
2+Y=4
» Y=2
Substitute Y=2 in Eqn 4 » Z=0
b.
10X + Y + Z = 12 ……… Eqn a
8X + 2Y +Z = 11 ………. Eqn b
20X - 10Y - 2Z = 8……... Eqn c
Eqn. a – Eqn b
» 2X-Y=1
Eqn c can be written as 10(2X-Y)-2Z=8
Substitute 2X-Y=1 in the above eqn
10(1)-2Z=8 » Z=1
Substitute Z=1 and Y=2X-1 in eqn a
10X+2X-1+1=12 » X=1 and Y=2(1)-1=1
c.
22X + 5Y + 7Z = 12 ……..Eqn 6
10X + 3Y + 2Z = 5 ………Eqn 7
9X + 2Y + 12Z = 14………Eqn 8
Multiply Eqn 6 by 2 and Eqn 7 by 3 and subtracting them
X={32(1-Z)}/7…..Eqn 9
Eqn 6-Eqn7-Eqn8 » 3X-7Z=-7
Substitute value of X in 3X-7Z=-7 » Z=1
Substitute Z=1 in Eqn 9 » X=0
Substitute X=0 and Z=1 in Eqn 6 » Y=1