Standard 5.1 Pre-Assessment 2

Transcription

1 Standard 5. Pre-Assessment Name: Date: For #-9, decide the number of solutions for each system of linear equations below. A. Solution B. No solution C. Infinitely Many Solutions x + y = x + y = 5. x 4y = 9x + y = 6. x = 5 x = 7. x + y = 6 y = x + 8. y = ( x 4) + 4x 8y = 4 9. x + y = 0 x y = 0 0. Given that x y = 9is one equation in a system. Determine another equation so that the system has: a. No Solution b. One Solution c. Infinitely Many Solutions. Explain what it means for a system to have infinitely many solutions.

2 For #-7, solve the system by graphing.. y = x 5 4 x = 4. 6 x + y = 8 y = ( x + ) x 4y = y = x y = y = 5 ( x ) 4 6. y = x + x + 8 y = 4x + 7. y x x = y = + ( x ) 8

3 For #8-, solve the system algebraically. 8. y = x 5 y = x x = y 9 x y = 0. 8 x 6 y = 4 x 9y = 6. y x x = + y = x 5. y = x x + 4 y = x + x y = x x y = x + 5 For # 5 0, solve the following by using a system of equations. 4. It takes a canoe hours to go 6 miles downstream but 8 hours to return home. What is the rate of the canoe and the rate of the current? 5. To make green paint, a painter mixes yellow paint and blue paint in the ratio of three to two. If he used twelve gallons of yellow paint, how much blue paint did he use? 6. Twice as many general admission tickets to a basketball game were sold as reserved seat tickets. General admission tickets cost $0 and reserved seat tickets cost $5. If the total ticket value of both kinds of tickets was $6,50, how many tickets of each kind were sold? 7. A plumber worked a total of 48 hours this week. He makes $0 per hour on a standard job and $5 per hour on a specialty job. This week he averaged $.5 per hour. How many hours did he work on specialty jobs? 8. Alley A charges $.5 per game of bowling and $.75 for shoe rentals. Alley B charges $ per game of bowling and $.75 for shoe rentals. Find the number of games for which the total cost is the same to bowl at either alley. 9. I am making a large bulletin board on my classroom wall which I will enclose with a fun border. I only have $6 to spend on the border. If the boarder cost $0.75 per foot and I want the height to be half the length, what should the bulletin board s dimensions be?

4 Answer Key ) B ) A ) C 4) A 5) A 6) B 7) A 8) C 9) A 0a) The equation x y = 9 can be rewritten as y = x which has a slope of / and a y-intercept of -. In order for our system to have No Solution the other equation must have the same slope but a different y-intercept so there are many possible answers in the form of x y = 9 y = x + # 0b) The equation x y = 9 can be rewritten as y = x which has a slope of / and a y-intercept of -. In order for our system to have One Solution the other equation must have a different slope so there are many possible answers. One example is x y = 9. y = x 0c) The equation x y = 9 can be rewritten as y = x which has a slope of / and a y-intercept of -. In order for x y = 9 our system to have Infinitely Many Solutions the other equation must have the same slope and y-intercept so or y = x any other equation that fits the pattern. ) A system has Infinitely Many Solutions when the two equations have the same slope and y-intercept. It DOES NOT mean that any ordered pair is a solution to the system. It means that any point on the line is a solution to the system and there are infinitely many points on the line. ) ) 4) (4, -) Infinitely Many Solutions No Solution 5) 6) 7) (0, 5) & (6, 5) (, 7) Infinitely Many Solutions

5 8) 48, 7 7 9) No Solution 0) Infinitely Many Solutions ) (-,-9)&(,-) ) (-, ) ) No Solution 4) the canoe is traveling 5 miles per hour & the current is miles per hour 5) 8 gallons of blue paint 6) 500 general admission tickets & 750 reserved tickets were sold 7) hours 8) 4 games 9) 8 feet by 6 feet