Question

Solve using the elimination method.

Answer 1

Answer:

x = (-15)

y = 6

z = 3

Step-by-step explanation:

x + y + z = -6______(1)

2x - y - 5z = -21____(2)

-x - y -6z = -9______(3)

(1) + (2)

$x + y + z + ( - x - y - 6z) = - 6 + ( - 9) \\ x + y + z - x - y - 6z = - 15 \\ - 5z = - 15 \\ z = \frac{ - 15}{ - 5} \\ z = 3$

z = 3, (1) + (2)

$x + y + 3 + (2x - y - 5z) = - 6 + ( - 21) \\ x + y + 3 +( 2x - y - 5( - 3) = - 27 \\ x + y + 3 + (2x - y + 15) = - 27 \\ x + y + 3 + 2x - y + 15 = - 27 \\ 3x + 18 = - 27 \\ 3x = - 27 - 18 \\ 3x = - 45 \\ x = \frac{ - 45}{3} \\ x = ( - 15)$

x = (-15), (1)

$x + y + z = - 6 \\ ( - 15) + y + 3 = - 6 \\ - 12 + y = - 6 \\ y = - 6 + 12 \\ y = 6$