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Chapter 1:
Graphing Systems of Equations
Chapter 2&3:
The Substitution and Elimination Method
Chapter 4:
Consistent and Inconsistent Systems
Chapter 5:
Systems of Inequalities
Chapter 6:
Classic Puzzles in Two Variables
100
Answer the following questions: a. Graph the system {(y=4x-1)/(y=-2x+2)┤ b. What does { mean when solving systems of equations?
a. What is (1/2, 1)? b. What are equations that form a system?
100
a. Solve by using substitution: {(4x+5y=23)/(x=1/2-2y)┤ b.Solve by using the Elimination method {(2x-y=4)/(x+y=2)┤
a. What is (-13.5, -7) or (-27/2,-7)? b. What is (2, 0)?
100
Complete the following statement: __________ and ________ systems are under _________ systems which are opposite of inconsistent equations.
What are dependent, independent, and consistent systems? *dependent and independent may be switched around, but not consistent
100
Solve and graph {(x+y<3)/(-x+y≥-2)┤
What are y<-x+3 and y≥+x-2…REFER TO GRAPH?
100
Basketball card A and basketball card B are 5 years older than basketball card A. In 3 years, basketball card B will be 2 times older than basketball card A. How old are both of the cards individually?
What is basketball card A that is 2 years old and basketball card B that is 7 years old?
200
Solve the system by graphing: {(x-3y=14)/(2x+y=7)┤
What is (5, -3)?
200
a. Solve by using elimination: {(3x-3/4 y=5)/(6x+3/4 y=7)┤ b. Solve by using the Elimination method {(4x+8y=16)/(8x+19y=47)┤
a. What is (4, -9 1/3) or (4, -28/3)? b. What is (-6, 5)?
200
What type of system is the following: {(4x+2y=7)/(2x+y=1)┤
What is an inconsistent system?
200
Solve and graph {(2x-2y<8)/(3x+1/2 y≥4)┤
What are y<-3x+4 and y≥-3/2x+2…REFER TO GRAPH?
200
A plane travels 350 mph against the wind. The plane traveled a total 1.740 miles, in 3 hours with the wind. If the plane traveled the same distance in 5 hours without the wind, find the speed of the plane and wind individually.
What is the plane that travels 464mph and the wind that is 116mph?
300
Find the approximate solution by graphing: {(y=9.2x+3)/(y=3x-4)┤
What is (1.0 — 1.4, -7.1 — -7.5)? *Give or take from (-1.1291, -7.3873)
300
a. Solve by using both substitution and elimination {(3y=4x-8)/(2.5x+5y=6.5)┤ b. Solve by using the Elimination method {(423x+123y=2430)/(123x+124y=1236)┤
a. What is (-2.36, -0.48) or (-59/25, -12/25)? b. What is (4, 6)?
300
What type of system is the following: {(2x+2y=4)/(2x4y=2)┤
What are consistent and independent systems?
300
Based on the graph, what is the system? REFER TO GRAPH
What is {(y≤4/3 x-3 1/2)/(y>-3/2 x+5)┤ or {(-4/3 x+y≤-3 1/2)/(3/2 x+y>5)┤ ?
300
The sum of a two digit number 6. The original two-digit number is less than twice of the two-digit number reversed. In fact, it is 3.5 times less than that. Hint: the number is less than 3.
What is 2.4?
400
Find the approximate solution by graphing: {(3.4x+y=4)/(-10.4x+5.2y=-8)┤
What is (0.7 — 0.9, 0.8 — 1.0)? *Give or take from (0.9302, 0.8372) and 0.6/ 0.7 (respectively) will be considered
400
a. A businessman sells a laptop and a touchscreen tablet. The tablet is $125 more than the laptop. The businessman will make $8,160,000 if he sells 8 of each item. How much money does each of the items cost? b. Solve by using the Elimination method {(2.7y=3.8x-2.3)/(3x-4y=4.7)┤
a. What is a tablet that costs $425 and a laptop that costs $300? b. What is x is about 3.08309856(0) and y is about 3.4873239(4)? *Rounding error expected, accuracy up to the hundredths digit (tenths digit will be considered).
400
True or false: It there are the same amount of the same variables (e.g. x) with the same coefficients (e.g. nx) on both the left and right hand side, then the system is inconsistent.
What is true?
400
At a carnival, Person A only hit 2-point balloons and 4-point balloons and got at least 8 points. He never got more than 12 points. Find the combinations of 2-point and 4-point balloons Person A could have hit.
What is {(x+y≤12)/(2x+4y≥8)┤ … REFER TO GRAPH?
400
A child has 1845 quarters and nickels in his piggy bank. If broken into the most coins possible, the value of the 1845 quarters and nickels would equal 136 half dollar coins and a quarter. How many quarters and nickels does the child have?
What are 900 quarters and 945 nickels?
500
The cost of a blue toy car is $4, while the cost of a red toy car is $7. A mother bought her child 8 cars and paid with $100. The amount the mother paid was $18 plus 2 times the cost. How many of each car did the mother buy?
What are 5 blue cars and 3 red cars?
500
5. A sport’s head board is purchasing awards. The cost of a trophy is three times plus $6 of the cost for a medal. The cost for a certificate is $7 and each participant gets a certificate. Last year’s tournaments cost the organization $5,355. This year, the cost will also be the same. There will be 10 champions and each champion will receive a trophy. The champion will also receive a medal. There are 3 types of medals total. If 645 athletes will participate, how much will a trophy and medal each cost?
What is a trophy that costs $45 and a medal that costs $13?
500
Answer the following: a. Perpendicular lines are ________ systems. b. After a system is solved (or attempted to be) and both the right and left hand side of the equation share the same value, the systems is _________. c. Systems with equations that have the same coefficient for x are ________ systems.
a. What are consistent and independent systems? b. What is dependent? c. What are inconsistent systems?
500
DAILY DOUBLE!! (answer the question and double the points/"money" you choose to bet!) ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ Gamer A plays a video game and earns 125 points. Gamer A plays a computer game and earns 350 points. Gamer A wants to earn at least 975. However, Gamer A does not want to get more than 1,100 because he knows it will him exhausted. Find the combinations of video and computer games Gamer A can earn.
What is {(x+y≤975)/(125x+550y≥1,100)┤ …REFER TO GRAPH?
500
A 3.47% sodium solution is mixed with a 5.34% sodium solution. How many fluid ounces is needed to produce 80 fluid ounces of 4.25% sodium solution?
What is the first solution which is about 46.6310(1) fluid ounces and the second solution which is about 33.369(9) fluid ounces? *Rounding error expected, accuracy expected up to the tenths digit.