Exercise 100 Page 598

The given system consists of equations of planes. Notice that the coefficient of

y

in the second equation is the same number as the coefficient of

y

in the third equation; they will subtract to be

0 .

Let's use the Elimination Method to find a solution to this system.

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ x - 2 y + 3 z = 8 2 x + y + z = 6 x + y + 2 z = 12 (I) (II) (III)

We can start by subtracting the third equation from the second equation to eliminate the

y - terms .

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ x - 2 y + 3 z = 8 2 x + y + z = 6 x + y + 2 z = 12 (I) (II) (III)

$(II):$ Subtract $(III)$

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ x - 2 y + 3 z = 8 2 x + y + z - (x + y + 2 z) = 6 - (12) x + y + 2 z = 12

$(II):$ Distribute $(- 1)$

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ x - 2 y + 3 z = 8 2 x + y + z - x - y - 2 z = 6 - 12 x + y + 2 z = 12

$(II):$ Subtract terms

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ x - 2 y + 3 z = 8 x - z = - 6 x + y + 2 z = 12