Question

Solve.

2x−y−4z=4
3x−2z=7
x−2y=−2

Enter your answer, in the form (x,y,z), in the boxes in simplest terms.

Answer 1

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Answer:

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

Explanation:

Most manual solutions to a system of 3 equations in 3 unknowns are ad hoc. The idea is to take advantage of any relationships that might exist between the coefficients.

Multiply the first equation by 2, then subtract the third equation.

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

4x -2y -8z -x +2y = 8 +2 . . . . . . . eliminate parentheses

3x -8z = 10 . . . . . simplify

Now, we can subtract this from the second equation:

(3x -2z) -(3x -8z) = (7) -(10)

6z = -3 . . . . . . . simplify

z = -1/2 . . . . . . . divide by 6

Using the second equation, we can find x:

3x -2(-1/2) = 7

3x = 6 . . . . . . . . subtract 1

x = 2 . . . . . . . . . divide by 3

Using the last equation, we can find y:

2 -2y = -2

1 -y = -1 . . . . . . divide by 2

y = 2 . . . . . . . . add y+1

The solution is ...

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