5.1
5.2
5.3
5.4
** Challenge**
100
You graph a system of linear equations, and the solution is (3,4). How can you verify that the solution is (3,4)?
You would solve it by substituting x and y into the linear equation to see if it equaled out. 
100
Solve the system of linear equations by substitution. Check your solution.


2x + 3y = 5

4x - y = 3 

(1,1)
100
Describe how to solve a system of linear equations by elimination. 
Multiply, if necessary, one or both equations by a constant so at least one pair of like terms has the same opposite coefficients.
100
Let x and y be two numbers. Find the solution of the puzzle.


y is 1/3 more than 4 times the value of x.

The difference of 3y and 12x is 1.

Infinitely many solutions; all points on the line y=4x+1/3
100
                        *** Daily Double ***

How can you use the slopes and the y-intercepts of equations in a system of linear equations to determine whether the system has one solution, infinite solutions, or no solution? Explain your reasoning.


When the slopes are different, there is one solution. When the slopes are the same, there is no solution if the y intercepts are different and infinite solutions if the y intercepts are the same. 
200
Solve the system of linear equations by graphing. 


y=2x+9

y=6-x

Show us how to do it on the graph board in our classroom.
200
Describe how to solve a system of linear equations by substitution. 
Solve one of the equations for one of the variables.
200
x+3y=5

-x-y=1

(2,1)
200
Tell whether the system of linear equations has one solution, infinitely solutions, or no solution.


y=8x-2

y-8x=-2


Infinite
200
ERROR ANALYSIS

  

5x + 2y = 9

3x - 2y = -1

  -----------------

2x            =10

X=5                               The solution is (5,-8)


The student added y-terms, but subtracted x-terms and constants; solution (1,2)
300
What is the slope of the line that passes through (-2,-2) and (3,-1)? 
1/5
300
Solve the system of linear equations by substitution.


y= 2x+5

y=3x-1

(6,17)
300
x+4y=1

3x+5y=10

(5,-1)
300
Solve.


y=3x+1

-x+2y=-3

(-1,-2)
300
A bouquet of lilies and tulips has 12 flowers. Lilies cost $3 each, and tulips cost $2 each. The bouquet costs $ 32. Write and solve a system of linear equations to find the number of lilies and tulips in the bouquet. 
x+y=12;

3x+2y=32;

(8,4); 8 lilies, 4 tulips

400
Solve the equation. And CHECK your solution.


5(2 - y) + y = -6

y=4
400
A drama club earns $1040 from a production. It sells a total of 64 adult tickets and 132 student tickets. An adult ticket costs twice as much as the student ticket.

                Write a system of linear equations that represents this situation.

64x + 132y = 1040

x=2y

400
2a+6=12

a+3=6

Tell whether the two equations are equivalent.

yes
400
Write an equation of the line that passes through the given points.


(0,0) (2,6)

y=3x
400
The price of 2 pears and 6 apples is $14. The price of 3 pears and 9 apples is $21. Can you determine the unit prices for pears and apples? Explain.
No solution; the lines have the same slope and different y- intercepts. 
500
Is it possible for a system of two linear equations to have exactly two solutions? Explain your reasoning.
No, Two lines cannot intersect in exactly two points.
500

             ** Daily Double **

An animal shelter has a total of 65 abandoned cats and dogs. The ratio of cats to dogs is 6:7. How many cats and dogs are in the shelter? Justify your answer.
30 cats : 35 dogs
500

                           *** Daily Double ***

You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in 22 minutes. 

         A) write a system of linear equations that represents this situation.

         B) How long does it take you to jog around the park?





A) 2x+y=10

     2x+3y=22

B) 6 minutes

500
You download a digital album for $10. Then you and your friend download the same number of individual songs for $0.99 each. Write a system of linear equations that represents this situation.
y=0.99x + 10

y=0.99x

500
Guest check #1         4 specials, 2 glasses of milk

                                              $28.00

Guest check #2         3 specials, 4 glasses of milk

                                             $ 26.25

How much does it cost for 2 specials and 2 glasses of milk?

                                              

$16.10
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