SOLUTION: Solve the following system of 3 equations. Be sure to indicate which is your working equation and which is your focus variable. 2x+4y-z=1 and 3x+3y+4z=1 and -5x-8y+6z=5.

Question 1109682: Solve the following system of 3 equations. Be sure to indicate which is your working equation and which is your focus variable. 2x+4y-z=1 and 3x+3y+4z=1 and -5x-8y+6z=5.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(1) 2x +4y -z = 1
:
(2) 3x +3y +4z = 1
:
(3) -5x -8y +6z = 5
:
multiply equation 1 by 6 and add it to equation 3
:
(4) 7x +16y = 11
:
multiply equation 1 by 4 and add it to equation 2
:
(5) 11x +19y = 5
:
equations 4 and 5 are two equations in two unknowns
:
solve equation 4 for x
:
x = (11 -16y)/7
:
substitute for x in equation 5
:
11*((11 -16y)/7) +19y = 5
:
((121 -176y)/7) +19y = 5
:
multiply both sides of = by 7
:
121 -176y +133y = 35
:
-43y = -86
:
y = 2
x = (11 -16(2))/7 = -3
:
use equation 1 to get the value for z
:
2(-3) +4(2) -z = 1
:
-6 +8 -z = 1
:
-z = -1
:
z = 1
:
*****************************************************
x = -3, y = 2, z = 1
:
check answers by substituting in equations 1, 2 and 3
:
(1) 2(-3) +4(2) -1 = 1
-6 +8 -1 = 1
1 = 1
:
(2) 3(-3) +3(2) +4(1) = 1
-9 +6 +4 = 1
1 = 1
:
(3) -5(-3) -8(2) +6(1) = 5
15 -16 +6 = 5
5 = 5
:
the answer checks
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