Systems in Three Variables
Authored by Anthony Clark
Mathematics
11th Grade
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20 questions
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1.
FILL IN THE BLANK QUESTION
1 min • 1 pt
Solve the system by elimination and write your solution as an ordered triple (r,s,t). If there is no solution, write "none". If there are an infinite number of solutions, write "infinite".
2.
FILL IN THE BLANK QUESTION
1 min • 1 pt
Solve the system by elimination and write your solution as an ordered triple (a,b,c). If there is no solution, write "none". If there are an infinite number of solutions, write "infinite".
3.
FILL IN THE BLANK QUESTION
1 min • 1 pt
Solve the system by elimination and write your solution as an ordered triple (x,y,z). If there is no solution, write "none". If there are an infinite number of solutions, write "infinite".
Answer explanation
The three planes representing the solution sets of each equation all meet at one point, shown in the picture. A system with solutions is called a CONSISTENT system.
4.
FILL IN THE BLANK QUESTION
1 min • 1 pt
Solve the system by elimination and write your solution as an ordered triple (x,y,z). If there is no solution, write "none". If there are an infinite number of solutions, write "infinite".
Answer explanation
The planes representing the solution sets of each equation do not all intersect, so there are no solutions. If you graphed the three planes, they would look like this. A system with no solutions is called an INCONSISTENT system.
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Solve the system.
(5, -6, 3)
(2, 3, -1)
(-4, 2, 5)
No Solution
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Solve the system.
(3, -2, 4)
(2, -3, 1)
(-3, 2, -1)
Infinitely many solutions
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Solve the system.
(1, 2, -2)
(1, -3, -2)
(-1, 3, 2)
No Solution
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