Question

5.
x + y + z = 1
2x + y +z = 2
x + 2y + 2z=1​

Answer 1

Step-by-step explanation:

1 Solve for xx in x+y-z=-2x+y−z=−2.

x=-2-y+zx=−2−y+z

2 Substitute x=-2-y+zx=−2−y+z into z+2x-y=5z+2x−y=5.

3z-4-3y=53z−4−3y=5

3 Substitute x=-2-y+zx=−2−y+z into -x+2y+2z=1−x+2y+2z=1.

2+3y+z=12+3y+z=1

4 Solve for zz in 2+3y+z=12+3y+z=1.

z=-1-3yz=−1−3y

5 Substitute z=-1-3yz=−1−3y into x=-2-y+zx=−2−y+z.

x=-3-4yx=−3−4y

6 Substitute z=-1-3yz=−1−3y into 3z-4-3y=53z−4−3y=5.

-7-12y=5−7−12y=5

7 Solve for yy in -7-12y=5−7−12y=5.

y=-1y=−1

8 Substitute y=-1y=−1 into x=-3-4yx=−3−4y.

x=1x=1

9 Substitute y=-1y=−1 into z=-1-3yz=−1−3y.

z=2z=2

10 Therefore,

\begin{aligned}&x=1\\&y=-1\\&z=2\end{aligned}

x=1

y=−1

z=2

Done