What is the solution to x+y-z=1 x+2z=0 2x+2y=4

EQ. 1: x+y-z = 1

EQ 2: x + 2z = 0

EQ. 3: 2x+2y=4

Solve for X in EQ. 2: x + 2z=0, subtract 2Z from each side:

x = - 2Z

Replace X in EQ. 1 with solution of EQ 2 and solve for Y:

-2z + y - z = 1

Simplify:

-3z + y = 1

Add 3z to each side::

y = 3z + 1

Replace X and Y in EQ. 3 and solve for Z:

2 (-2z) + 2 (3z+1) = 4

Distributive property:

-4z + 6z + 2 = 4

Simplify:

2z + 2 = 4

Subtract 2 from each side:

2z = 2

Divide both sides by 2:

z = 1

Now replace z with 1 and solve:

X = - 2z = - 2 (1) = - 2

Y = 3z + 1 = 3 (1) + 1 = 3+1 = 4

Z = 1

Solution is (-2,4,1)