Exercise 8 Page 165

The given system consists of equations of planes. Because at least one variable has a coefficient of

1

we will use the Substitution Method to solve this system of equations. When using this method it is necessary to isolate a variable. In the first equation, it will be easiest to isolate

y .

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ - 5 x + y - 4 z = 60 2 x + 4 y + 3 z = - 12 6 x - 3 y - 2 z = - 52 (I) (II) (III)

AddEqn

$(I):$ $LHS + (5 x + 4 z) = RHS + (5 x + 4 z)$

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y = 60 + 5 x + 4 z 2 x + 4 y + 3 z = - 12 6 x - 3 y - 2 z = - 52

With a variable isolated in one of the equations, we can substitute its equivalent expression into the remaining equations. In the final step of the simplification of these substitutions, our goal is to have yet another variable isolated.