Question 683913: Would you please help me solve this equation:
Solve the system analytically:
x+y+z=-4
2x+6y+2z=8
-x+7y-3z=40
Thanks Found 2 solutions by ankor@dixie-net.com, mananth:Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website! Solve the system analytically:
x + y + z= -4
2x+ 6y+ 2z = 8
-x+ 7y -3z = 40
:
Multiply the 1st equation by -2, add to the 2n equation
-2x + -2y + -2z = 8
2x + 6y + 2z = 8
--------------------adding eliminates x and z find y
4y = 16
y = 16/4
y = 4
:
Replace y with 4 in the 1st equation
x + 4 + z = -4
x + z = - 4 - 4
x + z = -8
:
In the 3rd equation, replace y with 4
-x + 7(4) - 3z = 40
-x - 3z = 40 - 28
-x - 3z = 12
Add to the 1st two unknown equation
-x - 3z = 12
x + z = -8
----------------adding eliminates x, find z
-2z = 4
z = 4/-2z
z = -2
:
Replace y and z in the 1st equation
x + 4 - 2 = -4
x = -4 - 2
x = -6
:
Summarize: x=-6; y=4; z=-2
:
:
You can check solutions in the 2nd equation
2(-6) + 6(4)+ 2(-2) = Answer by mananth(16946) (Show Source): You can put this solution on YOUR website! 1 x + 1 y + 1 z = -4 --------------1
2 x + 6 y 2 z = 8 -------------- 2
-1 x + 7 y + -3 z 40 -------------- 3
consider equation 1 &2 Eliminate y
Multiply 1 by -6 -5
Multiply 2 by 1 4
we get
-6 x + -6 y + -6 z = 24
2 x + 6 y + 2 z = 8
Add the two
-4 x + 0 y + -4 z = 32 ------------- 4
consider equation 2 & 3 Eliminate y
Multiply 2 by -7
Multiply 3 by 6
we get
-14 x + -42 y + -14 z = -56
-6 x + 42 y + -18 z = 240
Add the two
-20 x + 0 y + -32 z = 184 -------------5 5
Consider (4) & (5) Eliminate x
Multiply 4 by -5
Multiply (5) by 1
we get
20 x + 20 z = -160
-20 x + -32 z = 184
Add the two
0 x + -12 z = 24
/ -69840
z = -2
Plug the value of z in (5)
-20 x + -32 z = 184
-20 x = 120
x = -6 OR
plug value of x & z in 1
-6 + 1 y + -2 = -4
1 y = -4 + 6 + 2
y = 4
x=-6,y=4,z=-2