# How do you solve the system of equations algebraically y=x+2z, z=-1-2x, x=y-14?

Nov 1, 2017

Solution: $x = - 4 , y = 10 , z = 7$

#### Explanation:

y=x+2z (1) ; z= -1-2x (2) ; x=y-14 (3) :. y = x+14

Putting $y = x + 14$ in equation (1) we get $\cancel{x} + 14 = \cancel{x} + 2 z$

$\therefore 2 z = 14 \mathmr{and} z = 7$ Putting $z = 7$ in equation (2 ) we get

$7 = - 1 - 2 x \mathmr{and} 2 x = - 1 - 7 \mathmr{and} 2 x = - 8 \mathmr{and} x = - 4$

Putting $x = - 4 , z = 7$ in equation (1) we get

$y = - 4 + 2 \cdot 7 = - 4 + 14 = 10 \therefore x = - 4 , y = 10 , z = 7$

Solution: $x = - 4 , y = 10 , z = 7$ [Ans]