Case Study Class 9 Maths Linear Equations in Two Variables

Case Study Class 9 Maths Linear Equations in Two Variables

Case Study Class 9 Maths Linear Equations in Two Variables | Free Online Test

Case Study Class 9 Maths Linear Equations in Two Variables

Students preparing for exams often search for Case Study math questions for class 9. These exercises help strengthen concepts in the Linear Equations in two variables. Our online tests include interactive math case study questions class 9 that focus on real-life applications of numbers. Practicing these questions regularly improves accuracy and speed. Additionally, students develop problem-solving skills while applying formulas in practical situations.

Importance of Case Study of Linear Equations in two variables Class 9th

Math case study questions class 9 encourage analytical thinking and logical reasoning. For instance, questions on rational and irrational numbers allow deeper understanding. Furthermore, solving these problems enhances critical thinking. Short exercises help reinforce key formulas. Therefore, students gain confidence and clarity in the Linear Equations in two variables through consistent practice.

Benefits of Online Test Practice

Our math case study questions online tests provide instant feedback and performance tracking. Students can identify errors quickly and improve their approach. The Linear Equations in two variables case study questions class 9 cover various difficulty levels. Consequently, learners strengthen concepts efficiently and are better prepared for exams. Regular practice ensures mastery of fundamental Linear Equations in two variables topics.

Case Study 1: Linear Equations in Two Variables

In a local market, a shopkeeper sells pens and pencils. The cost of one pen is taken as Rs. 10 and the cost of one pencil is taken as Rs. 5. The shopkeeper notices that on a particular day, he sells a total of 30 items consisting of pens and pencils. The total revenue generated on that day amounts to Rs. 200. Representing the number of pens sold as $x$ and the number of pencils sold as $y$, we get a system of linear equations in two variables. Such problems are solved by forming equations from the given conditions and analyzing their solutions. A pair of linear equations in two variables is represented as \[ a_{1}x + b_{1}y + c_{1} = 0, \] \[ a_{2}x + b_{2}y + c_{2} = 0, \] where the solution may be consistent, inconsistent, or dependent based on the relation \[ \frac{a_{1}}{a_{2}}, \ \frac{b_{1}}{b_{2}}, \ \frac{c_{1}}{c_{2}}. \]

MCQ Questions

1. If the number of pens is $x$ and pencils is $y$, which equation represents the total items sold?

  • A) $x + y = 200$
  • B) $x + y = 30$
  • C) $10x + 5y = 200$
  • D) $10x + y = 30$
Answer: B) $x + y = 30$
Solution: Since total items sold are 30, equation is $x + y = 30$.

2. Which equation represents the total revenue generated?

  • A) $10x + 5y = 200$
  • B) $x + y = 200$
  • C) $5x + 10y = 200$
  • D) $10x + y = 200$
Answer: A) $10x + 5y = 200$
Solution: Total cost is 10 per pen and 5 per pencil. Hence, $10x + 5y = 200$.

3. Solving $x + y = 30$ and $10x + 5y = 200$, find the number of pens sold.

  • A) $20$
  • B) $10$
  • C) $15$
  • D) $5$
Answer: B) $10$
Solution: From $x + y = 30$, $y = 30 – x$. Substituting in $10x + 5y = 200$, \\ $10x + 5(30-x) = 200 \implies 10x + 150 – 5x = 200 \implies 5x = 50 \implies x = 10$.

4. With $x = 10$, how many pencils were sold?

  • A) $20$
  • B) $10$
  • C) $15$
  • D) $25$
Answer: A) $20$
Solution: From $x + y = 30$, $10 + y = 30 \implies y = 20$.

5. What type of solution does the pair of equations $x + y = 30$ and $10x + 5y = 200$ represent?

  • A) No solution
  • B) Infinitely many solutions
  • C) Unique solution
  • D) Parallel lines
Answer: C) Unique solution
Solution: Ratios: $\frac{a_{1}}{a_{2}} = \frac{1}{10}, \frac{b_{1}}{b_{2}} = \frac{1}{5}$, not equal. Hence, unique solution exists.

Your Results:

Correct Answers: 0

Incorrect Answers: 0

Percentage Score: 0%

Educational Resources Footer

Free Educational Resources

Free Study Material English Vocabulary Tests Grammar for Hearing Impaired Math for Hearing Impaired English Vocabulary Case Study Questions Math GRE Vocabulary Tests LaTeX Tutorial R Programming Tests Online English Games Online Math Games Learn Computer Basics JEE Math Tests CAT Quant Tests Increase Calculation Speed Class 10 Math Tests Prompt Engineering SAT Math Tutorial Logic Quizzes Grade 1 Logic Quizzes Grade 2

© 2023 Udgam Welfare Foundation. All rights reserved.