Graphing/Technology
Solving Systems by Substitution
Solving Systems by Elimination
Solving Systems of Inequalities
Word Problems
What method?/
How many solutions?
How many solutions?
100
What is the solution to the systems of equations?
(-1,1)
100
Solve the systems of equations using substitution:
-3x+4y=-2
y=-5
(-6,-5)
100
Solve the systems of equations using elimination:
14x+2y=26
-14x-6y=-50
(1,6)
100
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.
100
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
100
What method should you use for the following systems of equations?
3x-5y=10
7y-3x=25
Elimination
200
What is the solution to the systems of equations?
No Solutions
200
Solve the systems of equations using substitution:
-5x-5y=10
y=-4x-17
(-5,3)
200
Solve the systems of equations using elimination:
2x+y=7
x-2y=6
(4,-1)
200
When do you use a dotted line and when do you use a solid line when graphing inequalities?
Dotted: > or <
Solid: > or <
200
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
200
Which method would you use to solve the system of equations? Explain your reasoning.
y=4x-5
5+2x=y
Substitution, both equations already have y by itself so you just need to set the two equations equal to each other.
300
Using your graphing calculator or Desmos, find the solution to the systems of equations:
y=6x-11
-2x-3y=-7
(2,1)
300
Solve the systems of equations using substitution:
-8x-5y =-24
-x+y=10
(-2,8)
300
Solve the systems of equations using elimination:
-3x-24y=-66
3x+4y=-14
(-10,4)
300
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 equations that represents this scenario.
b+r≥3
4b+3r≤21
300
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.
300
How many solutions does the following system of equations have?
-7x - 5y = -8
8x - 3y = -17
(-1,3)
One Solution, different slopes
400
Using your graphing calculator or Desmos, find the solution to the systems of equations:
5x+3y=15
10x+6y=20
No Solution
400
Solve the systems of equations using substitution:
x+3y=1
-3x-3y=-15
(7,-2)
400
Solve the systems of equations using elimination:
2x+8y=6
-5x-20y=-15
Infinite Number of Solutions
400
Solve the system of equations by graphing:
y ≤ x − 2
y > −3x + 5
400
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.
400
How many solutions does the following system of equations have?
3x - y = 19
-3x + y = 10
No Solutions
500
Using your graphing calculator or Desmos, find the solution to the systems of equations:
2x+8y=6
-5x-20y=-15
Infinite number of solutions
500
Solve the systems of equations using substitution:
-2x+6y=6
-7x+8y=-5
(3,2)
500
Solve the systems of equations using elimination:
3+2x-y=0
-3-7y=10x
(-1,1)
500
Solve the systems of equations by graphing:
3x+2y≥-2
x+2y<2
500
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.
500
How many solutions does the following system of equations have?
3y+4x=6
12y+16x=24
These are the same exact line (same slope and same y-int), therefore they have Infinite Solutions.