The given system consists of equations of planes. Let's use the Elimination Method to find a solution to this system. Notice that in the third equation there is no

x -

term.

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 4 x - y + 2 z = - 6 - 2 x + 3 y - z = 8 2 y + 3 z = - 5 (I) (II) (III)

By manipulating the first equation and adding it to the second equation, we can solve for

y .

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 4 x - y + 2 z = - 6 - 2 x + 3 y - z = 8 2 y + 3 z = - 5 (I) (II) (III)

▼

(II):

Solve by elimination

MultEqn

$(II):$ $LHS \cdot 2 = RHS \cdot 2$

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 4 x - y + 2 z = - 6 - 4 x + 6 y - 2 z = 16 2 y + 3 z = - 5

SysEqnAdd

$(II):$ Add $(I)$

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 4 x - y + 2 z = - 6 - 4 x + 6 y - 2 z + (4 x - y + 2 z) = 16 + (- 6) 2 y + 3 z = - 5

RemovePar

$(II):$ Remove parentheses

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 4 x - y + 2 z = - 6 - 4 x + 6 y - 2 z + 4 x - y + 2 z = 16 - 6 2 y + 3 z = - 5

AddTerms

$(II):$ Add terms

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 4 x - y + 2 z = - 6 5 y = 10 2 y + 3 z = - 5

DivEqn

$(II):$ $LHS / 5 = RHS / 5$

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 4 x - y + 2 z = - 6 y = 2 2 y + 3 z = - 5

Exercise