Inequalities
Solving by Graphing
Solving by Elimination
Solving by Substitution
Word Problems
Anything Goes
100
Describe how you would shade y < 3x + 4
What is "underneath" or "where (0,0) is"?
100
The solution to the system of equations:
2x - 6y = 18
y = 1/3x - 3
What is all real numbers? (slope-intercept form of both equations is the same)
100
Use elimination to find the solution to the system of equations:
x + y = -6
x - y = -10
What is (-8, 2)?
100
Use substitution to find the solution to the system of equations:
x = 4y
2x + 3y = 22
What is (8, 2)?
100
The sum of two numbers is 104. Their difference is 68. What are the numbers?
Write the two equations for the system. Then find the solution.
What is
x + y = 104
and
x - y = 68
? What are 86 and 18?
100
Solve: 2(x – 3) = 4x + 1
What is x = -7/2?
200
Solve y < x + 2 and x > 3
(Make a makeshift graph to show your solution to the system and give a solution that works for the solution)
What is a graph with y < x + 2 shaded underneath and to the right of x > 3 with both having dotted lines?
200
The solution to the system of equations:
y = 3x - 2
y = -x - 2
What is (0, -2)?
200
Use elimination to find the solution to the system of equations:
8x + 5y = 9
2x - 5y = -4
What is (1/2, 1)?
200
Use substitution to find the solution to the system of equations:
y = x - 2
3x - y = 16
What is (7, 5)?
200
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660.
Write the two equations for the system. Then find the cost of one shirt.
What is
6x + 8y = 700
and
9x + 6y = 660
? What is x = $30?
200
Slopes of a line parallel and a line perpendicular to: 3x − 4y = 7
What is 3/4 (parallel) and -4/3 (perpendicular)?
300
Is (3, -4) a solution to 3x - y > 13?
What is no? (13 = 13 (not greater))
300
The solution to the system of equations:
y = -3
x = 5
What is (5, -3)?
300
Use elimination to find the solution to the system of equations:
2x + 3y = 6
3x + 5y = 15
What is (-15, 12)?
300
Use substitution to find the solution to the system of equations:
y = 3x - 1
7x + 2y = 37
What is (3, 8)?
300
The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.00 if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and they made $3500 total.
Write the two equations for the system. Then find the number of advanced tickets and game-day tickets.
What is
x + y = 600
and
5x + 7.5y = 3500
? What is 400 advanced tickets, 200 game-day tickets?
300
Find f(2)
What is f(2) = 1?
400
Which point IS in the solution of the system of inequalities?
A) (-2, -1) B) (0, -2) C) (0, -1) D) (0, 0)
What is C) (0,-1)?
400
The solution to the system of equations
y = (1/3)x - 3
2x - y = 8
What is (3, -2)?
400
Use elimination to find the solution to the system of equations:
2x - 4y = 12
-8x + 16y = -48
What is infinitely many solutions?
400
Use substitution to find the solution to the system of equations:
3x - 2y = 4
y = 2x - 1
What is (-2, -5)?
400
The dimensions of a rectangle whose perimeter is 78 inches, when the length of the rectangle is twice its width.
Write the two equations for the system. Then find the solution.
What is
2l + 2w = 78
and
l = 2w
? For the dimensions, what is 26 x 13?
400
Write an equation through (2, 1) and (4, 5)
What is y = 2x - 3?
500
Solve y >= 3/2x + 4 and y < 2/3x + 4
(Make a makeshift graph to show your solution to the system and give a solution that works for the solution)
What is a graph with y >= 3/2x + 4 with a solid line and shaded above and y < 2/3x + 4 with a dotted line and shaded below? No solutions.
500
The solution to the system of equations:
y - 3x = 3
y = 3x - 2
What is no solution? (slope-intercept form of both graphs has the same slope but not the same y-intercept
500
Use elimination to find the solution to the system of equations:
(1/3)x + (1/4)y = 10
(1/3)x - (1/2)y = 4
What is (24, 8)?
500
Use substitution to find the solution to the system of equations:
x + y = 12
x = (1/3)y
What is (3, 9)?
500
You need at least 3 pounds of fruit to make muffins. Blueberries cost $4 per pound and strawberries cost $3 per pound. You can spend at most $21 on fruit.
Write the two inequalities for the system. Then find an amount (in pounds) of berries and strawberries that you could get.
What is
x + y>= 3
for the amount of pounds you need and
4x + 3y <= 21
for the amount that fits in your budget?
500
Find x when f(x) = -3
What is x = 1?