Question 625770: 8x+2y-z=34
7x+3y-2z=40
3x-5y+z=24
Answer by Maths68(1474)   (Show Source):
You can put this solution on YOUR website! 8x+2y-z=34...............(1)
7x+3y-2z=40...............(2)
3x-5y+z=24...............(3)
Multiply (1) by -2 and add (2)
-16x-4y+2z=-68
7x+3y-2z=40
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-9x-y=-28...............(4)
Multiply (3) by 2 and add (2)
7x+3y-2z=40
6x-10y+2z=48
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13x-7y=88.................(5)
Multiply (4) by -7 and add (5)
63x+7y=196
13x-7y=88
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76x=284
Divide by 76 both sides of above equation
76x/76=284/76
x=71/19
Put the value of y in (5)
13x-7y=88.................(5)
13(71/19)-7y=88
13(71/19)-7y=88
923/19-7y=88
Multiply above equation by 19
19(923/19-7y)=19(88)
923-133y=1672
-133y=1672-923
-133y=749
Divide by -133 both sides of above equation
-133y/-133=749/-133
y=-107/19
Put the value of x and y in (1)
8x+2y-z=34...............(1)
8(71/19)+2(-107/19)-z=34
568/19-214/19-z=34
-z=34-568/19+214/19
Take LCD on Right hand side
-z=(646-568+214)/19
-z=(860-568)/19
-z=292/19
Multiply by (-) both sides of above equation
z=-292/19
x,y,z=71/19,-107/19,-292/19
Check
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Put the values of x,y and z in (1)
8x+2y-z=34...............(1)
8(71/19)+2(-107/19)-(-292/19)=34
568/19-214/19+292/19=34
Take LCD
(568-214+292)/19=34
(860-214)/19=34
646/19=34
34=34
Put the values of x,y and z in (2)
7x+3y-2z=40...............(2)
497/19-321/19+584/19=40
Take LCD
(497-321+584)/19=40
(1081-321)/19=40
760/19=40
40=40
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