Question

Solve the following 3 × 3 system. Enter the coordinates of the solution below.

2x – 3y – 2z = 4
x + 3y + 2z = –7
–4x – 4y – 2z = 10

Answer 1

9514 1404 393

Answer:

(x, y, z) = (-1, 0, -3)

Explanation:

We notice that the coefficients of z are such that elimination of the z term from the equations is made easy.

Adding equations 1 and 2:

(2x -3y -2z) +(x +3y +2z) = (4) +(-7)

3x = -3

x = -1

Adding equations 2 and 3:

(x +3y +2z) +(-4x -4y -2z) = (-7) +(10)

-3x -y = 3

Substituting for x, we get ...

(-3)(-1) -y = 3

0 = y . . . . . . . . . . . add y-3 to both sides

Then z can be found from any equation. Substituting for x and y in the second equation gives ...

-1 +2z = -7

2z = -6 . . . . . add 1

z = -3 . . . . . .divide by 2

The solution is (x, y, z) = (-1, 0, -3).