Graphing/Technology
Solving Systems by Substitution
Solving Systems by Elimination
Solving Systems of Inequalities
Word Problems
Challenge
200
What is the solution to the systems of equations?
(-1,1)
200
Solve the systems of equations using substitution:
-3x+4y=-2
y=-5
(-6,-5)
200
Solve the systems of equations using elimination:
14x+2y=26
-14x-6y=-50
(1,6)
200
What is the difference between solutions for systems of linear equations and systems of linear inequalities?
Systems of linear equations have one solution (unless no solution or infinite solutions). Systems of inequalities have many solutions.
200
Ms. Skweres bought 2 new shirts and a dress for $45. She then went back and bought another shirt and 4 dresses for $70.
Write a systems of equations for the situation.
2x+y=45
x+4y=70
200
TAKE ALL THE POINTS FROM ONE OTHER TEAM!
The point (2,5) is a solution to the system of equations below. Which of the following would it not be a solution to?
x+2y =12 and 3x-y=1
-2x+3y=11
6x-2y=2
4x+y=13
2x+4y=12
2x+4y=12
400
What is the solution to the systems of equations?
No Solutions
400
Solve the systems of equations using substitution:
-5x-5y=10
y=-4x-17
(-5,3)
400
Solve the systems of equations using elimination:
2x+y=7
x-2y=6
(4,-1)
400
When do you use a dotted line and when do you use a solid line when graphing inequalities?
Dotted: > or <
Solid: > or <
400
Ms. Blasi went to Dunkin and bought one coffee and a bagel, her total was $7. Ms. Redmond-Mattucci went to Dunkin and bought 2 coffees and 3 bagels for her and her friends and spent $18.
How much does one bagel cost?
One bagel costs $4
400
TRIPLE YOUR POINTS!
If the point (2,5) is a solution to the system of equations, then determine the missing values of b and m. Show all your work.
y=mx+9
y=3x+b
m=-2
y=3x-1
y=-2x+9
600
GIVE 200 POINTS TO ANOTHER TEAM!
Using your graphing calculator, find the solution to the systems of equations:
y=6x-11
-2x-3y=-7
(2,1)
600
Solve the systems of equations using substitution:
-8x-5y =-24
-x+y=10
(-2,8)
600
Solve the systems of equations using elimination:
-3x-24y=-66
3x+4y=-14
(-10,4)
600
LOSE ALL YOUR POINTS IF YOUR TEAM IS INCORRECT!
You need at least 3 pounds of fruit to make muffins. Blueberries cost $4 per pound, raspberries cost $3 per pound, and you have only $21. If b represents blueberries (in pounds) and r represents raspberries (in pounds), write a systems of inequalties that represents this scenario.
b+r≥3
4b+3r≤21
600
Mr. Perez tells his class that the next test is worth 100 points and contains 28 problems. Multiple-choice questions are worth 3 points each and word problems are worth 4 points each. How many of each type of questions are in there?
Let x be the number of multiple choice questions and y be the number of word problems.
(12,16)
There are 12 multiple-choice questions and 16 word problems.
600
How many solutions does the following system of equations have?
-7x - 5y = -8
8x - 3y = -17
(-1,3)
One Solution, different slopes
800
Using your graphing calculator, find the solution to the systems of equations:
5x+3y=15
10x+6y=20
No Solution
800
DOUBLE YOUR POINTS!
Solve the systems of equations using substitution:
x+3y=1
-3x-3y=-15
(7,-2)
800
Solve the systems of equations using elimination:
2x+8y=6
-5x-20y=-15
Infinite Number of Solutions
800
Solve the system of equations by graphing:
y ≤ x − 2
y > −3x + 5
800
Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. On Saturday night, there were 321 total tickets sold for $937.50. How many adult tickets were sold? How many student tickets were sold?
Let x be the number of adult tickets sold and y be the number of student tickets sold.
(135, 186)
There were a total of 135 adult tickets sold and 186 student tickets sold.
800
Would the point (5,10) lie in the solution set of the system of inequalities below?
x>2
y>=3x-7
Yes.
10>=8
5>2
1000
Using your graphing calculator, find the solution to the systems of equations:
2x+8y=6
-5x-20y=-15
Infinite number of solutions
1000
Solve the systems of equations using substitution:
-2x+6y=6
-7x+8y=-5
(3,2)
1000
Solve the systems of equations using elimination:
3+2x-y=0
-3-7y=10x
(-1,1)
1000
Solve the systems of equations by graphing:
3x+2y≥-2
x+2y<2
1000
Daniella broke her piggy bank open and found that it only contained quarters and pennies. She counted 120 coins with a grand total of $16.32.
How many pennies did Daniella have in her piggy bank?
Daniella had 57 pennies in her piggy bank.
1000
Solve the inequalities for y.
Is (3,2) in the solution set?
6x-3y<=-9
x + y <6
No
y>=2x+3
y<-x+6