Question 1014596
x-6y-2z=-8
-x+5y+3z=2
3x-2y-4z=18
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x-6y-2z=-8
-x+5y+3z=2
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 -y+z= -6
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x-6y-2z=-8
3x-2y-4z=18
On the first equation multiply all terms by -3:
-3x+18y+6z= 24 
Add the equations:
-3x+18y+6z= 24
3x-2y-4z= 18
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16y+2z= 42
Now we have two new equations:
-y+z= -6
16y+2z= 42
Multiply the 1st equation times -2
2y-2z= 12
Add equations
16y+2z= 42
2y-2z= 12
18y= 54 Divide both sides by 18
y= 3 Now we know the value of y.
Take one of the last two equations and find z:
16y+2z= 42
16(3)+2z= 42
48+2z= 42
2z= -6
z= -3
You say, what if I chose the other equation to find z? Well:
2y-2z= 12
2(3)-2z= 12
6-2z= 12
-2z= 6
z= -3 Same answer. Cool, no?
Now we know y and z, let's go back to one of the original equations to find x:
x-6y-2z=-8
x-6(3)-2(-3)= -8
x-18+6= -8
x-12= -8
x= 4
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Am I right? Let's check:
x-6y-2z=-8; 4-6(3)-2(-3)= -8; 4-18+6= 8; -18+10= -8 Correct
-x+5y+3z=2; -4+5(3)+3(-3)= 2; -4+15-9= 2; 11-9= 2 correct
3x-2y-4z=18; 3(4)-2(3)-4(-3)= 18; 12-6+12= 18; 6+12= 18 Correct
We have the correct answers.
J