Reporting Strand 4: Systems of Equations & Inequalities Subunit 4a: Solving Systems of Equations
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
A.REI.6/A.CED.2/A.CED.4 Levels 1 - 3 Solve the following systems of equations & inequalities by graphing. 1. 3𝑥 − 2𝑦 = 6 2. 2𝑥 − 𝑦 = 1 𝑥 + 𝑦 = 2 4𝑥 − 2𝑦 = 2
3. 𝑦 = 2𝑥 + 1 4. 𝑦 = −4𝑥 + 5 𝑦 = 2𝑥 − 3 𝑦 = 3𝑥 − 9
5. 𝑦 = −3𝑥 + 7 6. 𝑥 + 3𝑦 = 6 𝑦 = 2𝑥 − 3 𝑥 − 3𝑦 = 6
Solve the following systems of equations using the substitution method. 7. – 𝑥 + 2𝑦 = 4 8. 5𝑥 − 𝑦 = 1 5𝑥 − 3𝑦 = 1 3𝑥 + 2𝑦 = 13 9. 𝑥 = 5 − 𝑦 10. 4𝑥 + 𝑦 − 8 = 0 2𝑥 + 7𝑦 = 0 5𝑥 + 3𝑦 − 3 = 0
Solve the following systems of equations using the elimination method. 11. 3𝑥 + 𝑦 = 10 12. 3𝑥 − 2𝑦 = 1 2𝑥 − 𝑦 = 5 8𝑥 + 3𝑦 = 2 13. 5𝑥 − 2𝑦 = 30 14. 9𝑥 + 8𝑦 = 15 𝑥 + 2𝑦 = 6 9𝑥 + 8𝑦 = 30
Level 4 15. Cadence has a collection of 52 dolls that all have either blue eyes or green eyes. Cadence has 16 more blue-‐eyed dolls than green-‐eyed dolls.
16. Dalton has 7 bills, all tens and twenties, that total $100 in value. How many of each bill does he have? 16. Eldora and Finn went to an office supply store together. Eldora bought 15 boxes of paper clips and 7 packages of index cards for a total cost of $55.40. Finn bought 12 boxes of paper clips and 10 packages of index cards for a total cost of $61.70. Find the cost of one box of paper clips and the cost of one package of index cards.
17. Galina spent $3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the number of 30¢ stamps. How many stamps of each kind did Galina buy? 18. Harold had a summer lemonade stand where he sold small cups of lemonade for $1.25 and large cups for $2.50. If Harold sold a total of 155 cups of lemonade and collected a total of $265, how many cups of each type did he sell?