7.1: Graphing Systems of Equations
7.2: Substitution
7.3: Elimination Using Addition and Subtraction
7.4: Elimination Using Multiplication
7.5: Graphing Systems of Inequalities
Word Problems
100
State whether the systems of equations has
ONE SOLUTION, NO SOLUTION or INFINITE MANY
y=-3/2x + 5
y=-2/3x +5
One Solution
100
Use Substitution!!! to solve each system of equations
y = 5x + 1
4x + y = 10
(1,6)
100
Use ELIMINATION to solve each system of equations.
-x + y = 7
x + y = 1
(-3, 4)
100
Use elimination to solve each systems of equations
x + y = 2
-3x + 4y = 15
( 1 , -3 )
100
Solve each system of inequalities by graphing.
y<6
y>x+3
Indicate 2 points that would be included in the solution
Desmos--graph
(0,5)
(-1,3)
(there are many others)
100
DOUBLE POINT QUESTION!
A child ticket costs $14 and a senior citizen ticket costs $8.
200
DOUBLE POINT QUESTION!
Does the below system of equations have
One solution, No solution or Infinitely Many solutions?
x+y=4
3x+3y=12
INFINITE MANY
200
Use Substitution!!! to solve each system of equations
y = -3x + 4
-6x -2y = -8
Infinitely many
200
Use ELIMINATION to solve each system of equations.
-4x + 5y = 17
4x + 6y = -6
(-3 , 1 )
200
Use elimination to solve each systems of equations
2x + 5y = 11
4x + 3y = 1
( -2 , 3 )
200
DOUBLE POINT QUESTION! Solve each system of inequalities by graphing.
y < x + 10
y > 6x + 2
Indicate 2 points that would be included in the solution.
Desmos-graph
200
The difference of two numbers is 3 and their sum is 13. What are the numbers?
What are 8 and 5.
300
DOUBLE POINT QUESTION! Write the system of equations in slope intercept form
state whether it has one, no, or infinite solutions
3x+6=y
y = 6
y=3x+6 & y=6
One solution
300
DOUBLE POINT QUESTION!
Use Substitution!!! to solve each system of equations
5x - y = 5
-x + 3y = 13
(2,5)
300
DOUBLE POINT QUESTION!
Use ELIMINATION to solve each system of equations.
a + 4b = -4
a + 10b = -16
( 4 , 2 )
300
Use elimination to solve each systems of equations
12x - 3y = -3
6x + y = 1
( 0 , 1 )
300
Solve each system of inequalities by graphing on Desmos.
x + y < -1
x + y > 3
Indicate 2 points that would be included in the solution.
Desmos--graph
300
Write a system of equations and solve. If you get this problem correct, you can have another turn.
Small box is $7 and large box is $13
400
Write the system of equations in slope intercept form
state whether the system has one, no, or infinite solutions
2x+5=y
4x +10 = 2y
y=2x+5
y=2x+5
Infinite many
400
Use Substitution!!! to solve each system of equations
y = 3x + 2
2x + 2y = 20
(2 , 8)
400
Solve using elimination. If you get this problem correct, you can have another turn!
2x + y = -8
x - y = 2
( -2 , -4 )
400
Mr. Santos, the curator of the children's museum, recently made two purchases of firing clay and poly clay for a visiting artist to sculpt. On Tuesday he bought 5 bogs of firing clay and 24 boxes of poly clay for $64.05. On Wednesday he bought 25 bags of firing clay and 8 boxes of poly clay for $51.45.
Create the systems of equations to represent this situation.
5x + 24y = 64.05
25x + 8y = 51.45
400
y < x + 2
y > x - 3
Solve the system of inequalities by graphing. Indicate 2 points that would be included in the solution.
Desmos-graph
400
DOUBLE POINT QUESTION!
You need at least 3 lbs of fruit to make muffins. Blueberries cost $4 per lb and and strawberries cost $3 per lb. And you can spend at most $21.
Write and graph a system of inequalities. identify one solution.
x + y > = 3
4x + 3y < = 21
500
State whether the systems of equations is
ONE SOLUTION, NO SOLUTION or INFINITE MANY
2x + y = 4
y = -2x -2
no solution
500
DOUBLE POINT QUESTION!
Use Substitution!!! to solve each system of equations
y = -10x -1/2
-50x - 10y = 105
(2, -4 1/2)
500
Jeremy and Kendrick each bought snacks for their friends at a skating rink. Jeremy bought 4 bags of popcorn and 2 plates of nachos for $18.50. Kendrick bought 7 bags of popcorn and 2 plates of nachos for $26.75
Write the systems of equations.
4x + 2y = 18.50
7x + 2y = 26.75
500
2x + 3y = 13
x + y = 7
Solve the above system of equations
( 8 , -1 )
500
Graph the below system of inequalities
25x + 15y > 100
x + y < 6
desmos Graph
500
To prepared for your Thanksgiving football game, you head to the store to buy hamburgers and chicken. Hamburgers cost $2 per lb and chicken $3 per lb. You expect to buy at least 3 lbs of hamburgers. You have no more than $30 to spend. Write a system of inequalities to represent this situation. Graph on Desmos. Identify and interpret 2 solutions.
2x + 3y <= 30
x >=3
x = lbs of hamburgers
y = lbs of chicken