elimination
substitution
graphing
vocabulary
systems of inequalities
Random
100
x + 3y = 7
8x - 3y = 2
(1,2)
100
y = 5x - 1
2y = 3x + 12
(2,9)
100
y = 2x + 2
y = x - 1
(3,-4)
100
what are 3 methods of solving systems of equations?
elimination
graphing
substitution
100
when graphing linear inequalities do we use a solid or dotted line when the problem has < and >
Use a Dotted Line
100
Given the systems of equations
is (3,-1) a solution? Why or why not?
y = -2/3 x + 1
2x + 5y = 6
No it is not a solution because it does not make both equations true.
200
4x - 3y = 16
5x + 3y = 20
(4,0)
200
y = 3x
2x + y = 10
(2,6)
200
y = 2x + 5
y = x + 3
(-2,1)
200
y = 2x + 3
y = 2x - 5
Lines with the same slope have:
A) one solution
B) no solution
C) infinite solutions
200
what does ≤ and ≥ mean when graphing linear inequalities
solid line
200
Given the systems of inequalities
is (3,-1) a solution? Why or why not?
y >= -2/3 x + 1
2x + 5y < 6
Yes is is a solution because it makes both inequalities true.
300
-2x - 9y = -25
-4x - 9y= 23
(-1,3)
300
x - y = 10
y = 5 + x
no solution
300
3x - 2y = 8
x + y = 6
(4,2)
300
How can you tell if a linear system has infinitely many solutions?
the equations are the same and the lines lie on top of each other
300
y ≤ x − 2
y > −3x + 5
300
Bill went to the movies and bought himself and his family somethings to eat. Each soda pop cost $7 and each candy bar cost $5. If he spent $58 on 10 items, how many of each item did she buy.
- Solve the story problem and explain what the solution means. Be sure to use words in your explanation from the story problem and label your answers.
This means we can buy 4 popcorns and 6 candy bars and they will cost exactly $58. We also have exaclty 10 items if we buy 4 popcorns and 6 candy bars.
400
4x - 9y = 2
12x - 5y = -38
(-4,-2)
400
2x - 3y = -2
y= -4x + 24
(5,4)
400
4x - 5y = 15
8x + 5y = 45
(5,1)
400
What are the three possible solutions in a system of equations and how do you write them (abreviate)
A) one solution (x,y)
B) no solution
C) infinite solutions
400
How is graphing systems of inequalities different than graphing systems of equations?
they use dotted lines sometimes and you have to shade to find the solution
400
Bob gets a really good discount and buys movie tickets for $4 each and popcorn for $3 each, but he can spend no more than $27.
- Set up the linear inequality from the story problem and graph the linear inequality solution set. Label your graph!
- Give one specific solution of this inequality and explain what it means. Label your answer!
Any ordered pair in the shaded region will work. For example 2 movie tickets and 3 popcorns works.
To explain what it means: 2 movie tickets and 3 popcorn will cause Bill to spend no more than $27.