1. Graph the system of equations and tell the solution. 1. Solution
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1 Algebra Reporting Strand 4: Systems of Equations & Inequalities Subunit 4a: Solving Systems of Equations Review Name: Period: Date: Read all the directions carefully, put your answers in the blanks provided, and SHOW YOUR WORK!!! NO WORK = NO CREDIT CCSS 4-Mastery 3-Proficient 2-Basic 1-Below Basic 0-No Evidence Solve Systems of Equations (A.REI.6, A.CED.2, A.CED.4) Meets all of the criteria in a Level 3 Completes tasks including synthesis and evaluation or in context of a new situation Solve a system of linear equations in two variables using all of following methods: Graphing (standard form) Substitution Elimination (both equations need to be multiplied) Solve a system of linear equations in two variables using all of following methods: Graphing (slope intercept form) Substitution Elimination (one equation needs to be multiplied) Solve a system of linear equations in two variables using 2 of following methods: Graphing (slope intercept form) Substitution (one variable solved for) Elimination Little evidence of reasoning or application to solve the problem Does not meet the criteria in a level 1 1. Graph the system of equations and tell the solution. 1. Solution 3x y = 2 4y = x + 5
2 Solve each system by graphing. 2. y= 3x+7 x+ 1 2 y=1 3. x+2y=0 3x+2y= y 2x=1 y=2x+6 5. y=x+3 y=5x
3 Solve each system using substitution. 6. 2x y= 8 3x y= 9 4x 2y= x y= x=y+2 2y=1 3x 9. x=2y 2 3y=x
4 Solve each system using elimination x+5y=16 3x 5y= x y=4 9x+y= x+y=9 x+2y=11 3x= 18+4y y=58+5x
5 14. 8x+4y=20 7x+6y= x 8y= 22 5x 3y= Given the equation 3x + 9y = 8, write a second linear equation to create a system that: a. Has exactly one solution. Explain your reasoning. b. Has no solution. Explain your reasoning. c. Has infinitely many solutions. Explain your reasoning.
6 17. Interpret the meaning of the solution, if it exists, in the context of the graph of the following systems of equations. 5x + 2y = 10 10x 4y = A theaters charges $9 for each adult ticket & $6 for each children ticket. The theater sold 144 tickets for the first showing of a new released movie. The total money collected from tickets sales for that show was $1,164. Write a system of equations that could be used to find the number of children tickets and the number of adult tickets sold, and solve the system algebraically. Solution: 19. Tim has a collection of 12 CDs and Nina has a collection of 18 CDs. Tim is adding 4 CDs a month to his collection while Nina is adding 3 CDs a month to her collection. Write a system to describe this situation. Then find the number of months after which they will have the same number of CDs. Solution:
7 20. A corner store sells two kinds of baked goods: cakes and pies. A cake costs $4 and a pie costs $9. In one day, the store sold 13 baked goods for a total of $87. Write a system to describe this situation. Then find out how many cakes and pies did they sell? Solution: 21. At the local ballpark, the team charges $5 for each ticket and expects to make $1,200 in concessions. The team must pay its players $1,900 and pay all other workers $1,400. Each fan gets a free bat that costs the team $1 per bat. How many tickets must be sold to break even? Solution: 22. Denise has $1.95 in her pocket made up of 27 nickels and dimes. How many of each type of coin does she have? Solution:
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