Question

HELP WILL MEDAL!
-x+y-2z=-5
5x+4y-4z=4
x-3y-2z=3
so far i have y=1
I know the answer is x=-4 y=1 z=-5 but I don't know where to go from where I am.

Answer 1

x-3y-2z=3
-x+ y+2z=-5
-2y =-2
-2 =-2 Divided by -2
y=1

Answer 2

replace \(y\) by \(1\) in any two of the three equations
then you will have two variables with two equations to solve

Answer 3

take 2 of the 3 equations, it does not matter which 2, and eliminate a variable
-x + y - 2z = -5
x - 3y - 2z = 3
-----------------add
-2y - 4z = -2

now take 2 equations, make sure you get the equation you have not messed with yet, and eliminate THE SAME variable
-x + y - 2z = -5 --->(5)
5x + 4y - 4z = 4
---------------
-5x + 5y - 10z = -25 (result of multiplying by 5)
5x + 4y - 4z = 4
---------------add
9y - 14z = - 21

now take your 2 answers and eliminate a variable
-2y - 4z = -2 --->(9)
9y - 14z = -21 --->(2)
---------------
-18y - 36z = -18 (result of multiplying by 9)
18y - 28z = - 42 (result of multiplying by 2)
--------------add
- 64z = - 60
z = -60/-64
z = 15/16

now enter 15/16 in for z in an equation that you eliminated the x out of
-2y - 4z = -2
-2y - 4(15/16) = -2
-2y - 60/16 = -2
-2y = 60/16 - 2 ---> common denominator is 16
-2y = 60/16 - 32/16
-2y = 28/16
y = (28/16) / -2
y = 28/16 * -1/2
y = - 28/32
y = - 7/8

now sub 15/16 in for z and -7/8 in for y in one of the original equations
-x + y - 2z = -5
-x + (-7/8) - 2(15/16) = -5
-x - 7/8 - 30/16 = -5
-x - 14/16 - 30/16 = -5
-x - 44/16 = -5
-x = 44/16 - 5 --> common denominator is 16
-x = 44/16 - 80/16
-x = - 36/16
x = 36/16
x = 9/4

you can then check your answers by subbing in to one of your original equations
x - 3y - 2z = 3
9/4 - 3(-7/8) - 2(15/16) = 3
9/4 + 21/8 - 30/16 = 3 ---> common denominator is 16
36/16 + 42/16 - 30/16 = 3
78/16 - 3016 = 3
48/16 = 3
3 = 3 (correct)

so x = 9/4, y = -7/8, and z = 15/16

I do not know where you got your answers from....unless the problem is written incorrectly

Answer 4

x should equal -4
y should equal 1
z should equal -5

Answer 5

lets check that...
if x = -4 and y = 1 and z = -5

-x + y - 2z = -5
-(-4) + 1 - 2(-5) = -5
4 + 1 + 10 = -5
15 = -5 (this is incorrect)

Those are not the answers to your problem

Answer 6

x-3y-2z=3
-x+y+2z=-5
______________
-2y = -2
divide by -2
y=1

Answer 7

5(-x+y+2z=-5)
5x+4y-4z=4
________________
-5x+5y+10z=-25
5x+4y-4z=4
_________________
9y+6z=-2
9(1)+6z=-21
9+6z=-21
-9 =-9
6z=-30
Divide by 6 z=-5

Answer 8

-x+y+2z=-5
-x+(1)+2(-5)=-5
-x+1-10=-5
-x-9=-5
+9=+9
-x = 4
-*1 = *-1
x = -4

Answer 9

you wrote the problem wrong...in the original way it is posted, you have all 3 z's as being negative