Parallel, Intersecting, or Same Line
Solving by Graphing
Solving by Substitution
Solving Using Elimination
Choosing the Best Method
Applications of Systems of Equations
100
Determine if the graph shows a system of linear equations that is intersecting, parallel, or the same line.
State how many solutions there are for the system.
Intersecting
One solution
100
Decide whether the given ordered pair is a solution of the system of equations.
y=2x-1
y=1/3x+4
(3,5)
Yes
100
Solve the system of equations using the substitution method.
x=y+1
3x+2y=18
(4,3)
100
Transform the system of linear equations into a system that is ready for columns to be added together to eliminate a variable OR rewrite the system if it already set up for elimination.
3x-y=3
6x+2y=9
6x-2y=6
6x+2y=9
100
State the best method to solve the system of linear equations and then solve.
2x+y=6
x-y=6
Elimination
(4,-2)
100
Answer the question by setting up and solving a system of equations.
Two jet ski rental companies have different costs. Company A charges a flat fee of $8 plus $2.50 per hour. Company B charges a flat fee of $14 plus $1.00 per hour. At what point in time are both rentals the same amount? How much are the rentals for that amount of time?
y=2.5x+8
y=x+14
(4,18)
After 4 hours the rentals cost the same amount of $18.
200
Determine if the graph shows a system of linear equations that is intersecting, parallel, or the same line.
State how many solutions there are for the system.
Same line
Infinitely many solutions
200
Decide whether the given ordered pair is a solution of the system of equations.
y=x-2
4x+y=-2
(0,-2)
Yes
200
Solve the system of equations using the substitution method.
y=-4x+1
y=2x+13
(-2,9)
200
Solve each system of equations using the elimination method.
x+3y=17
2x-3y=-20
(-1,6)
200
State the best method to solve the system of linear equations and then solve.
x=y-1
3x+y=13
Substitution
(3,4)
200
Answer the question by setting up and solving a system of equations.
The Mendenhall Theater sells two types of tickets: youth and adult. The theater holds a total of 450 people. One night, the theater sold all their tickets for total of $2,706. Youth tickets cost $4.60 and adult tickets cost $7.00. How many tickets of each type did the theater sell that night?
x+y=450
4.6x+7y=2,706
(185,265)
The theater sold 185 youth tickets and 265 adult tickets.
300
Determine if the graph shows a system of linear equations that is intersecting, parallel, or the same line.
State how many solutions there are for the system.
Parallel
No solutions
300
Solve each system of equations by graphing.
y=1/2x-3
y=x-5
(4,-1)
300
Solve the system of equations using the substitution method.
-3x+y=9
y=2x+6
(-3,0)
300
Solve each system of equations using the elimination method.
5x+4y=22
2x+4y=16
(2,3)
300
State the best method to solve the system of linear equations and then solve.
y=1/3x-5
y=-4/3x
Graphing
(3,-4)
300
Answer the question by setting up and solving a system of equations.
Jamal and Emily each started a savings account in January. Jamal started with $46 in his account and added $24 each month. Emily opened her account with $319. Each month she withdrew $15. After how many months will they have the exact same amount in their accounts? How much will be in their accounts at that time?
y=24x+46
y=-15x+319
(7,214)
After 7 months they will both have $214 in their accounts.
400
Algebraically determine if the two lines in the system of equations are intersecting, parallel, or the same line.
State how many solutions there will be for the system and explain why.
y=-1/2x-4
y=1/2x+4
Intersecting
One solution
Different slopes
400
Solve each system of equations by graphing.
y=-1/3x
y=1
(-3,1)
400
Solve the system of equations using the substitution method.
x+y=3
x+2y=1
(5,-2)
400
Solve each system of equations using the elimination method.
2x+y=7
4x-3y=-6
(1.5,4)
400
State the best method to solve the system of linear equations and then solve.
3x+4y=7
x-8y=0
Elimination
(2,1/4)
400
Answer the question by setting up and solving a system of equations.
Two girls sold lemonade together. The entire lemonade sale brought in $28. One girl made $4 more than twice the amount the second girl made. How much did each girl make at the lemonade sale?
x+y=28
x=2y+4
(20,8)
One girl made $20 while the other made $8.
500
Algebraically determine if the two lines in the system of equations are intersecting, parallel, or the same line.
State how many solutions there will be for the system and explain why.
-6x+3y=12
y=2(x+1)+2
Same line
Infinitely many solutions
Same slopes and same y-intercepts
500
Sandra and Terry each walk to the same school from different neighborhoods. They do not cross paths until they reach the school building. Sandra follows the path represented by the equation
y=-2x+10
and Terry follows the path represented by the equation
y=-1/6x-1
What are the coordinates of the school building?
(6,-2)
500
Create and solve the system of equations that represents this situation using the substitution method.
Both of Monique's neighbors owned cows. Mr. James owned five less than three times the number of cows owned by Mr. Peters. The total number of cows owned by both neighbors was 79. How many cows did each neighbor own?
Let x represent the number of cows Mr. James owns and y represent the number of cows Mr. Peters owns.
x=3y-5
x+y=79
(58,21)
Mr. James = 58 cows
Mr. Peters = 21 cows
500
Patrick bought one baseball cap and one t-shirt for $36. Sammy bought two baseball caps identical to Patrick's caps along with three of the same t-shirts. Sammy spent a total of $94.
Create and solve the system of equations to match this situation and solve using the elimination method.
What are the individual costs for a t-shirt and a baseball cap?
x+y=36
2x+3y=94
(14,22)
Baseball Cap = $14
T-shirt = $22
500
State the best method to solve the system of linear equations and then solve.
y=1/2x+3
-3x+4y=18
Substitution
(-6,0)
500
GOOD JOB ON FINDING THE ONE FREEBIE!
BONUS 500 POINTS!