Graphing
Describe the graph for a 3x3 system of equations with ONE SOLUTION
What is all 3 planes will intersect at 1 point
Explain how to solve a system with graphing?
What is graph the equations and find the point(s) of intersection.
−x − 5y − 5z = 2
4x − 5y + 4z = 19
x + 5y − z = −20
What is (−2, −3, 3)
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)
What is isolating a variable and substituting it into the original equation to solve for the other variable. Substitute the found variable into the equation to find the other.
x − 6y + 4z = −12
x + y − 4z = 12
2x + 2y + 5z = −15
What is (0, 0, −3)
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
Explain how to solve using elimination
What is lining up the variables in the equations and manipulating the equations to eliminate a variable. Solve the remaining variable. Then substitute into the original equation to solve the other.
5a + 5b + 5c = −20
4a + 3b + 3c = −6
−4a + 3b + 3c = 9
What is no solutions
Draw an example of a 3x3 system with infinitely many solutions
See graph
For what might you use systems of linear equations for in the real world?
What is whether you'll make more money from one job or another (money and percentage), at what time you'll reach a destination with friends who are traveling at different speeds and different starting locations (speed, time, distance), geometry, physics (force and pressure), etc
2x-y+2z=6
-x+y+z=0
-x-3z=-6
What is infinitely many solutions
Draw an example of a 3x3 system with no solutions
See graph
Explain the logic/steps to solving a 3x3 system of linear equation.
What is lining up the variables, manipulating the equations to eliminate 1 variable and two 2x2 system, solve 2x2 system, plug back in to new equation then original equation to find remaining variables
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