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.