System of Equations Word Problems
Authored by Domenica Abbott
Mathematics
9th - 12th Grade
CCSS covered
Used 1K+ times
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This quiz focuses on systems of linear equations, covering both word problem applications and graphical solution methods appropriate for high school Algebra I students, typically grades 9-10. The questions assess students' ability to translate real-world scenarios into mathematical systems, solve equations using multiple methods, and interpret solutions graphically. Students need a solid foundation in linear equations, including slope-intercept form and standard form, along with strong problem-solving skills to identify variables and set up equations from contextual situations. The core concepts include understanding that a system's solution represents the intersection point of two lines, recognizing when systems have one solution, no solution, or infinitely many solutions, and applying algebraic manipulation techniques such as substitution and elimination. Students must also demonstrate proficiency in graphing linear equations and interpreting coordinate pairs as solutions to systems. Created by Domenica Abbott, a Mathematics teacher in the US who teaches grades 9-12. This comprehensive quiz serves multiple instructional purposes, from introducing students to systems of equations through engaging word problems to reinforcing solution strategies through varied practice. Teachers can use this as a formative assessment tool to gauge student understanding before moving to more complex applications, or as a review activity before summative assessments. The mix of word problems and graphical analysis makes it excellent for homework assignments that require students to practice both conceptual understanding and computational skills. The quiz effectively supports classroom instruction by providing immediate feedback on student comprehension of key concepts. This assessment aligns with Common Core standards A-REI.6 (solving systems of linear equations) and A-CED.3 (representing constraints by systems of equations), while also addressing Mathematical Practice standards MP1 (problem solving) and MP4 (mathematical modeling) through the real-world application problems.
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20 questions
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1.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations represents the situation?
4x + 2y = 44
x + y = 44
4x = y + 15
x - y = 15
Tags
CCSS.HSA.CED.A.3
2.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?
13.5x - 13y = 6
x - y = 6
3x + 7y = 13.5
3x - 7y = 13.5
Tags
CCSS.HSA.CED.A.3
3.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
The sum of Mr. Micklow and Ms. Craft's age is 55. The difference is 3.
Solve:
x + y = 55
x - y = 3
Tags
CCSS.8.EE.C.8C
4.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?
Oatmeal Cookies $3
Oatmeal Cookies $8
Oatmeal Cookies $6
Oatmeal Cookies $6
Tags
CCSS.8.EE.C.8C
5.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?
Tags
CCSS.8.EE.C.8C
6.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. How many students were on each van and each bus?
Bus 14
Bus 21
Bus 43
Bus 45
Tags
CCSS.8.EE.C.8C
7.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket.
Child $5
Child $6
Child $16
Child $13
Tags
CCSS.8.EE.C.8C
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