Step 6 It appears that the ordered triple is the only solution of the
system. We must check that the solution satisfies all three original equations
of the system. We begin with equation (1).
CHECK (1)
Substitute.
Multiply.2 = 2 ✓True
- 12 + 8 + 6 2
41 - 3 )+ 8112 + 6 2
4 x+ 8 y+z= 2
1 - 3 , 1 , 62
SECTION 4.2 Systems of Linear Equations in Three Variables 229
NOW TRY
EXERCISE 1
Solve the system.
- 3 x- 4 y+ 9 z=- 10
3 x+ 2 y+ 7 z= 8x- y+ 2 z= 1Write the values of x, y,
and zin the correct order.In Exercise 2you are asked to show that also satisfies equations (2)
and (3). The solution set is 51 - 3, 1, 6 26.
1 - 3, 1, 6 2
NOW TRYOBJECTIVE 3 Solve linear systems (with three equations and three vari-
ables) in which some of the equations have missing terms.If a linear system
has an equation missing a term or terms, one elimination step can be omitted.
Solving a System of Equations with Missing TermsSolve the system.
(1) Missing z
(2) Missing x
(3) Missing ySince equation (3) is missing the variable y, one way to begin is to eliminate y
again, using equations (1) and (2).
Multiply each side of (1) by 2.
Multiply each side of (2) by 3.12 x + 3 z=- 10 Add. (4)
24 y+^3 z=^0
12 x- 24 y =- 10
9 x- z = 12
8 y+ z = 0
6 x- 12 y=- 5
EXAMPLE 2
Leave space for
the missing term.Use the resulting equation (4) in xand z, together with equation (3), , to
eliminate z. Multiply equation (3) by 3.
Multiply each side of (3) by 3.
(4)
Add.or Divide by 39; lowest terms
We can find zby substituting this value for xin equation (3).
(3)LetMultiply.z= - 6 Subtract 6. Multiply by - 1.
6 - z= 12
9 a x=^23.
2
3
b - z= 12
9 x- z= 12
2
3
x=
26
39
,
39 x = 26
12 x+ 3 z=- 10
27 x- 3 z= 36
9 x-z = 12
NOW TRY ANSWER
- 51 2, 1, 0 26