Question

Hey i need help

Find the solution to this system of equations.

x − y + 2z = 0
x − 2y + 3z = -1
2x − 2y + z = 1

X=
Y=
Z=

PLEASE HELP

Answer 1

X = 4/3

Y = 2/3

Z = - 1/3

Explanation:

Multiply the first equation by -1 =

-x + y - 2z = 0

Add this equation to the second equation =

(x-2y+3z = - 1) + (-x + y - 2z = 0) =

-y + z = -1

Multiply the first equation by -2=

-2x+2y-4z = 0

Add this equation to the third equation =

(-2x+2y-4z=0) + (2x-2y+z=1) =

-3z = 1

z = - 1/3

(-y + z = - 1 ) = -y - 1/3 = -1

-1/3 + 1 = y

y = 2/3

Substitute z = -1/3 and y = 2/3 in an equation to find the x value.

x - 2/3 + 2(-1/3) = 0

x -2/3 - 2/3 = 0

x -4/3 = 0

x = 4/3

Answer 2

Explanation:

x−y+2z=0

Step 1: Add y to both sides.

x−y+2z+y=0+y

x+2z=y

Step 2: Add -2z to both sides.

x+2z+−2z=y+−2z

x=y−2z

Answer:

x=y−2z

x−2y+3z=−1

Step 1: Add -x to both sides.

x−2y+3z+−x=−1+−x

−2y+3z=−x−1

Step 2: Add -3z to both sides.

−2y+3z+−3z=−x−1+−3z

−2y=−x−3z−1

Step 3: Divide both sides by -2.

−2y/−2 = −x−3z−1/−2

y= 1/2 x+ 3/2 z+ 1/2

Answer:

y= 1/2 x+ 3/2 z+ 1/2

2x−2y+z=1

Step 1: Add 2y to both sides.

2x−2y+z+2y=1+2y

2x+z=2y+1

Step 2: Add -z to both sides.

2x+z+−z=2y+1+−z

2x=2y−z+1

Step 3: Divide both sides by 2.

2x/2 = 2y−z+1/2

x=y+ −1/2 z+ 1/2

Answer:

x=y+ −1/2 z+ 1/2