Graphing
Substitution
Elimination
Special Systems
Inequalities
100
Tell whether the pair is a solution. ( 0,-5) y = -6 + 5 x-y = 5
no it doesn't work
100
Solve by Using Substitution y = x + 3 y = 2x + 12
( -9, -6)
100
____________ type(s) of elimination can be used when no coefficients can cancel out immediately. ( 2 answers)
a) subtraction b) multiplication
100
___________ is a system with only one solution.
Independent System
100
The _______ consists of all the ordered pairs that satisfy all the inequalities in a system? A) System of Linear Equations B) Solution of a System of Linear Inequalities C) Linear Equation D) Dependent system
B- a Solution of a System of Linear Inequalities
200
Solve by Graphing. y = 3x + 2 y = -2x -3
Crosses at ( -1, -1)
200
Solve using Substitution y = -4x y = 2x-3
( 1/2 , -2)
200
Solve through elimination 4x + y = 1 2x - y = -5
( -1, 3)
200
How many solutions do the below systems have? y = 1/4 x - 3 y = 1/4 x + 5
No solution. These lines have the same slope.
200
What does the shaded region of a linear inequality show?
The shaded region shows all the possible answers for a solution of linear inequalities.
300
What is the solution of the graph? **Powerpoint slide one for graph.**
( -3, -3)
300
Solve through substitution 4x = 16y -28 -y -2x = 8
(-5, 2)
300
Solve through Elimination 5x - 2y = -15 2x - 2y = -12
( -1, 5)
300
How many solutions do these systems have? How do you know? -4x - y = 6 1/2 y = -2x - 3
There are infinitely many solutions. They have the same slope and y intercepts, therefore making them the same line.
300
Graph the inequality x + y + 4 > 0
Powerpoint page 2.
400
Solve by Graphing: -5 + y = -1/3 x 2x - 2y = -2
Crosses at (3,4)
400
Solve Through substitution 4y - 2x = -2 x + 3y = -4
( -1, -1)
400
Solve through Elimination -3x - 3y = 3 2x + y = -4
( -3, 2 )
400
Classify the type of system. Give the number of solutions for this system. 3x - 13 = 2y -3y = 2x
The system is consistent and independent. There is only one solution
400
The math club is selling pizza and lemonade to raise money for a trip. They estimate the trip to be $450. They earn $ 2 on each slice of pizza and a $1 on each bottle of lemonade. A) Write the inequality ( in simplest form) b) Graph the inequality. C) What are two possibilities of lemonade and pizza they can have? D) what are two possibilities that won't work for them to meet their goal.
A) x = slices of pizza, y = bottles of lemonade. 2x + y > or equal to 450 B) Powerpoint slide pg 3 c) possible answers: ( 200 slices, 50 bottles) and ( 150 slices, 150 bottles) D) 100 of each. or 100 slices of pizza, 300 bottles
500
solve by graphing x + 2y = -3 3x + 2y = 2
Crosses at (2, -2)
500
Solve by substitution 7x + y = -15 -6x -7y = -24
( -3, 6)
500
Solve through elimination ( 3 mins to solve) 3x = 6y = 0 7x + 4y = 20
( 4, 2 )
500
Classify each system. Give the number of solutions. 3y + 6x = 9 2( y - 3) = -4x
Consistent, dependent, with infinitely many solutions.
500
Graph the systems of inequalities. Give two possible outcomes that will work and two that won't. y < or equal to -2x + 8 y > 3x - 5
Graph on powerpoint slides. POssible answers that work ( 0, 0) and ( -5, 0) possible answers that don't work (8, 0) and ( 3, -3)
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