Question

Solve the system. x – 4y – z = 21 6x – 3y – z = –4 –x +2y –5z = 19 Answer: x =      , y =      , z =

Answer 1

Consider the given equations:

`-x+2y-5z = 19` (Equation 1)

`6x-3y-z= -4` (Equation 2)

`x-4y-z=21` (Equation 3)

Adding equations 1 and 3, we get

`-x+2y-5z+x-4y-z = 19+21`

`-2y-6z = 40`

So, we get
`-y -3z = 20` (Equation 4)

Multiplying equation 3 by '6', we get

`6x - 24y-6z = 126` (Equation 5)

Subtracting equation 5 from equation 2, we get

`(6x-3y-z)-(6x - 24y-6z) = -4-126`

`6x-3y-z-6x + 24y+6z) = -4-126`

`21y+5z = -130` (Equation 6)

Multiplying equation 4 by '21' and adding it to equation 6, we get

`-21y-63z+21y+5z = 420-130`

`-58z = 290`

So, z = -5

Since,
`-y-3z = 20`
`-y+15=20`
`y=-5`

So, y=-5

Now,
`x-4y-z=21`
`x-4(-5)-(-5)=21`
`x+20+5=21`
`x+25=21`
`x= -4`

So, x = -4

Therefore, x = -4, y= -5 and z= -5 are the solutions to the given equations.