Quick review:
They need two tickets for ride on the bumper cars and 3 tickets for each ride on the ferris wheel for a total of ten tickets. They went on 4 rides altogether.
First,
Two tickets for ride on the bumper cars and 3 tickets for each ride on the ferris wheel for a total of ten tickets. can be translated into algebra:
Where
x = # of rides on the bumper cars and
y = # of rides on the ferris wheel
2x + 3y = 10
Now the first part of our word problem is represented as a linear function. If we wanted, we could graph this function with the help of a table. The line would represent all the solutions that work.
Next,
They went on 4 rides altogether. Assuming the same variables x and y, we can place this equation underneath our original.
2x + 3y = 10
x + y = 4
These two formulas represent to linear functions that together make a system of equations.
Then, we can solve by any number of options:
- by graphing and identifying the point where the two lines cross
- by substituting
- x + y = 4 can be changed into x = y - 4
- we can then substitute the x in the first equation
- 2 (y - 4) + 3y = 10 and
- solve for y, then use our solution for y to help solve for x
- by multiplying and eliminating
- we can multiply the second equation by -3
- -3 (x + y = 4) becomes -3x + -3y = -12
- we can use that to eliminate the y in the first equation and
- solve for y, then use our solution for y to help solve for x
On Friday, we will have a quiz practicing these three options for solving. I will find systems of equations, give you the answers to them and then ask you to show your understanding of all three of these processes for solving them.
Today we will practice the last two methods.
Please start with practicing substituting. Watch the video of me solving #18 if you need any help.
HW: pg 386 #18*, 19, 20
Then watch the videos of me solving #3 on page 401 and #17 on 402. Take notes and then solve the remaining two by multiplying and eliminating.
HW: pg 401-2 #3*, 4, 5 and #17*, 18, 19
No comments:
Post a Comment