Systems in Three Variables

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".

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".

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.

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.

Solve the system. 

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution

Solve the system.

• (3, -2, 4)

• (2, -3, 1)

• (-3, 2, -1)

• Infinitely many solutions

Solve the system.

• (1, 2, -2)

• (1, -3, -2)

• (-1, 3, 2)

• No Solution

Solve the system.

• (2, -2, 3)

• (2, 1, 4)

• (-2, 2, -3)

• No Solution

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".

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

If you graph these three equations, you'll find that the three planes intersect along a line, so the system has an infinite number of solutions. A system of equations that has an infinite number of solutions is called a DEPENDENT system. It is also CONSISTENT, because it has solutions.