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DO NOW
DO NOW
Imagine there are tHREE PLANES. Be prepared to discuss the following:
Imagine there are tHREE PLANES. Be prepared to discuss the following:
- Could it be that these planes never intersect (touch)? How?
- Could be it that all three of them intersect at a single point? How?
- Could it be that they intersect an infinite number of times? How?
LEARNING TARGET
LEARNING TARGET
I can solve systems of linear equations in three variables using substitution or elimination.
I can solve systems of linear equations in three variables using substitution or elimination.
I DO
I DO
How do you solve a system of equations in three variables?
How do you solve a system of equations in three variables?
You use elimination or substitution to solve for one variable, then repeat to solve for the others.
You use elimination or substitution to solve for one variable, then repeat to solve for the others.
How would i know if my system has one solution, no solutions, or infinitely many solutions?
How would i know if my system has one solution, no solutions, or infinitely many solutions?
- If you find a value for x, y, and z using substitution or elimination, your system has one solution (a point)
- If you find a false equivalency, such as 0 = 7, then your system has no solutions
- If you find a true equivalency, such as 2 = 2, then your system has infinitely many solutions
Let's try An example:
Let's try An example:
4x + 2y + 3z = 12
4x + 2y + 3z = 12
2x - 3y + 5z = -7
2x - 3y + 5z = -7
6x - y + 4z = -3
6x - y + 4z = -3
WE DO
WE DO
For today's We Do, try to work this problem with another student. As you work, take turns narrating and listening.
For today's We Do, try to work this problem with another student. As you work, take turns narrating and listening.
NARRATOR: Works the problem on paper and says out loud what they are doing at each step
NARRATOR: Works the problem on paper and says out loud what they are doing at each step
LISTENER: Watches and listens as the narrator works, and asks questions about any step they don't agree with or don't understand
LISTENER: Watches and listens as the narrator works, and asks questions about any step they don't agree with or don't understand
You can switch roles between each "part" of the problem
You can switch roles between each "part" of the problem
The problem:
x + y - 2z = 5
x + y - 2z = 5
-x + 2y + z = 2
-x + 2y + z = 2
2x + 3y - z = 9
2x + 3y - z = 9
YOU DO
YOU DO
EXIT TICKET
EXIT TICKET
Can you think of a real world application for linear systems?
Can you think of a real world application for linear systems?
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