QuestionDetermine whether the ordered triples listed are solutions of the system of linear equations. (a) (b)
Studdy Solution
STEP 1
1. We have a system of three linear equations with three variables: , , and .
2. We need to determine if each ordered triple is a solution to the system by substituting the values into each equation.
3. An ordered triple is a solution if it satisfies all three equations.
STEP 2
1. Substitute the ordered triple (1, 1, -1) into each equation and verify.
2. Substitute the ordered triple (3, 1, -2) into each equation and verify.
STEP 3
Substitute into the first equation :
Simplify:
The first equation is satisfied.
STEP 4
Substitute into the second equation :
Simplify:
The second equation is satisfied.
STEP 5
Substitute into the third equation :
Simplify:
The third equation is satisfied.
Since all three equations are satisfied, the ordered triple is a solution.
STEP 6
Substitute into the first equation :
Simplify:
The first equation is satisfied.
STEP 7
Substitute into the second equation :
Simplify:
The second equation is not satisfied.
Since the second equation is not satisfied, the ordered triple is not a solution.
The ordered triple is a solution, while is not a solution.
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