Question

Solve the system by substitution

Answer 1

Answer:

  (x, y, z) = (-3, 2, 5)

Step-by-step explanation:

Using the first equation, we can write an expression for x:

  x = 21 +3y -6z

Substituting this into the remaining two equations gives ...

  3(21 +3y -6z) +2y -5z = -30

  63 +9y -18z +2y -5z = -30

  11y -23z = -93

and

  2(21 +3y -6z) -5y +2z = -6

  42 +6y -12z -5y +2z = -6

  y -10z = -48

This second equation makes it easy to write an expression for y:

  y = 10z -48

Substituting that into the previous equation, we have ...

  11(10z -48) -23z = -93

  110z -528 -23z = -93

  87z = 435

  z = 5

  y = 10(5) -48 = 2

  x = 21 +3(2) -6(5) = -3

The solution is (x, y, z) = (-3, 2, 5).