- Graph the following pairs of equations.
- For each set, answer the following questions.
- Do the graphs have any points in common? If so, how many?
- Compare the slopes of each graph.
- What is the relationship between the slopes and the number of points in common?
- Copy and complete the table below.
Description of Lines / How many points of intersection? / Equal Slopes? (yes/no) / Same Y-Intercept (yes/no)
Intersecting / Either
Parallel
Coinciding
System of Equations: A set of two or more equations that use the same variable.
Solution to a System: A set of values that that makes ALL equations true.
Is (-3, 4) a solution to the system?
Types of Solutions
One Unique Solution
Intersecting Lines
Many Solutions
Same (Coincidental Lines)
No Solution
Parallel Lines
A 15-minute long-distance telephone call costs $.90.The cost varies
directly as the length of the call. Write an equation that relates the
cost to the length of the call. How long is a call that costs $1.32?
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Classwork: ______
GRAPHING CALCULATOR
Enter Equations in Y=
Enter ZOOM 6
2nd TRACE
5 .INTERSECT
ENTERENTERENTER
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You are choosing between two long distance phone companies. Company Lessie charges $0.09 per minute plus a $4 fee. Company Levi charges $0.11 per minute and no monthly fee. Set up a system representing the cost ,y, based on the number of minutes, x, used.
After how long will the cost of the two long distance providers be the same?
Your family is planning a two day vacation. You estimate the cost of Virginia to be $200 per day. The cost of Tennessee is $250 per day. Your total budget for the 7 days is $1500. Set up a system representing the number of days you can spend in each city. You will use all the money and go to both cities.
How many days should you spend in each?
Solve the following system.
How can use algebraically solve this system?
(HINT: Transitive Property)
Or
______Property
Y = Y
2x-7 = 3x -7
-x = 0
x = 0
Solution to a system is a point (x,y).
x = 0
y = 2(0)- 7
y = -7
Solution is (0, -7)
Check your solutions!!!
This method is called SUBSTITUTION!
.
Linear Combinations/Elimination Process
Add or Subtract equations to eliminate a
variable.
Opposites must exist to Add/Subtract the Equations!
Solve
5x = 10
X = 2
Find y, using substitution.
Solution is (2, ½)
Opposites may not always exist! We can multiply the equation(s) to create opposites!
Special Solutions
True Statement = Many Solutions
False Statement = No Solution
Mrs. Doolittle has 10 cats and dogs. To board all of her animals costs $104 per day. If the kennel charges $8 per day to board a cat and $14 for a dog, how many cats and dogs does she have?
Laden sells 450 pounds of scrap aluminum and copper to a recycling plant for $234. he gets $0.40 per pound for his aluminum cans and $0.60 per pound for her copper tubing. How much copper and aluminum did he sell?
Mr. Beckwith buys a bag of apples and a bag of pears for a total of $14. There are eight pounds of fruit in all. The apples cost $1.50 per pound and the pears cost $2.30 per pound. How many pounds of pears and apples did he buy?
Sixty wedding guests are given a choice of steak or chicken. The bride and groom will be billed $30 for each steak dinner and $20 for each chicken dinner. If the total bill is $1470, how many guests had chicken? Steak?
Postcard stamps cost 20 cents each while letter stamps cost 33 cents each. If you have 50 stamps worth $12.60, how many of each type do you have?
Your school committee is planning a trip for 193 people. There are eight drivers and two types of vehicles. The buses seat 51 people and the vans seat 8. How many buses and vans will be needed?
Suppose your class sells gift wrap for $4 per package and greeting cards for $10 per package. Your class sells 205 Packages in all and receives a total of $1084. Find the number of packages of greeting cards sold.
Suppose your community center sells a total of 292 tickets for a basketball game. An adult ticket cost $3. A student ticket cost $1. The sponsors collect $470 in ticket sales. Find the number of each type of ticket sold.
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