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DO NOW
DO NOW
Imagine there are two lines on a coordinate plane. Be prepared to discuss the following:
Imagine there are two lines on a coordinate plane. Be prepared to discuss the following:
- How could it be that these lines never intersect (touch)?
- How could be it that they intersect only one time?
- How could it be that they intersect an infinite number of times?
DO NOW
DO NOW
without actually solving, can you tell how many solutions these systems have?
without actually solving, can you tell how many solutions these systems have?
- y = 5x - 2 and y = 5x + 3
- y = -x + 3 and x + y = 3
LEARNING TARGET
LEARNING TARGET
I can solve systems of linear equations in two variables using substitution or elimination.
I can solve systems of linear equations in two variables using substitution or elimination.
I DO
I DO
What does it mean to solve a system of equations?
What does it mean to solve a system of equations?
okay, but what if my name is west and/or i don't want to graph them to find the solution?
okay, but what if my name is west and/or i don't want to graph them to find the solution?
We use elimination or substitution to find the solution algebraically. Let's take a look:
ELIMINATION
ELIMINATION
Try to get on of the two variables to cancel. You can multiply or divide both sides of the equation by something to make this magic happen!
SUBSTITUTION
SUBSTITUTION
Solve one of the equations for one of the variables, then plug that back into the other equation so that equation now has only ONE variable. Now, you can solve it!
Let's try some examples:
Let's try some examples:
- -5x + 3y = 8 and 5x + 2y = 2
- 4x + 2y = 5 and 4x - y = -4
- x + y = 10 and 3x + 4y = 40
WE DO
WE DO
YOU DO
YOU DO
Page 1 of each is assigned. Completing problems from the back will earn extra credit
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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