PreCal 3x3 Sys of Eq

Graphing

100

Describe the graph for a 3x3 system of equations with ONE SOLUTION

What is all 3 planes will intersect at 1 point

200

Describe the graph(s) for a 3x3 system of equations with INFINITELY MANY SOLUTION

What is where all 3 planes intersect at 1 line or all three planes are the same (so they overlap everywhere)

300

Describe the graph(s) for a 3x3 system of equations with NO SOLUTION

What is where all 3 planes are parallel, 2 planes are parallel, or all the planes intersect at 3 distinct lines

400

Draw an example of a 3x3 system with infinitely many solutions

See graph

500

Draw an example of a 3x3 system with no solutions

See graph

Solve 3x3

100

−x − 5y − 5z = 2 

4x − 5y + 4z = 19 

x + 5y − z = −20

What is (−2, −3, 3)

200

x − 6y + 4z = −12 

x + y − 4z = 12 

2x + 2y + 5z = −15

What is (0, 0, −3)

300

5a + 5b + 5c = −20 

4a + 3b + 3c = −6 

−4a + 3b + 3c = 9

What is no solutions

400

2x-y+2z=6

-x+y+z=0

-x-3z=-6

What is infinitely many solutions

{(x,y,z)|x=-3z+6,y=-4z+6,zinRR}

500

Write a system of equations with the solution (2, 1, 0).

What is many answers. Ex: x + y + z = 3, 2x + y + z = 5, x + 2y − z = 4