Question

Find the solution to this system of equations x+y=1
2x-y+z=1
x+2y+z=8/3

Answer 1

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Answer:

(x, y, z) = (1/3, 2/3, 1)

Explanation:

We can use the first equation to write an expression for x that can be substituted into the other equations.

x = 1 -y

2(1 -y) -y +z = 1 ⇒ -3y +z = -1

(1 -y) +2y +z = 8/3 ⇒ y +z = 5/3

Subtracting the first of these equations from the second gives ...

(y +z) -(-3y +z) = (5/3) -(-1)

4y = 8/3

y = 2/3

z = 5/3 -y = 1

x = 1 -y = 1/3

The solution is (x, y, z) = (1/3, 2/3, 1).