use elimination to solve the system of equations x-y+z=-1, x+y+3z=-3 and 2x+y+2z=0

Question

you must use elimination to solve.

Answer 1

Elimination method

Given equations are x-y+z = -1 ---> (1)

x+y+3z = -3 ---> (2)

2x+y+2z = 0 ---> (3)

Multiple to each side of equation (2) by negitive 2.

-2x-2y-6z = 6 ---> (4)

To eliminate the x value subtract (1) from (2).

x+y+3z = -3

x-y+z  = -1

(-)(+)(-) (+)

__________

2y+2z = -2 ---> (5)

To eliminate the x value add (4)&(3).

-2x-2y-6z = 6

2x+y+2z = 0

__________

-y-4z = 6 ---> (6)

Multiple to each side of equation (6) by 2.

-2y-8z = 12 ---> (7)

To eliminate the y value add (7)&(5).

-2y-8z = 12

2y+2z = -2

_________

-6z = 10

z = 10/-6

⇒ z = -5/3

Put z in (6).

-y-4(-5/3) = 6

-y+20/3 = 6

y = 20/3 -6

⇒ y = 2/3

Put y,z in (1).

x-2/3-5/3 = -1

x = 2/3+5/3-1

⇒ x = 4/3

Solution x = 4/3, y = 2/3, z = -5/3.