Linear & Simultaneous Equations for Competitive Exams

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Linear & Simultaneous Equations

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Linear & Simultaneous Equations MCQ & Objective Questions

Linear and simultaneous equations are fundamental concepts in mathematics that play a crucial role in various exams. Mastering these topics can significantly enhance your problem-solving skills and boost your confidence during exams. Practicing MCQs and objective questions on linear and simultaneous equations helps you identify important questions and reinforces your understanding, making it easier to score better in your assessments.

What You Will Practise Here

Understanding linear equations and their graphical representation
Solving simultaneous equations using substitution and elimination methods
Identifying the slope-intercept form and point-slope form of linear equations
Applying real-life scenarios to formulate linear equations
Exploring systems of equations and their solutions
Analyzing word problems related to linear equations
Utilizing key formulas and definitions for quick reference

Exam Relevance

Linear and simultaneous equations are frequently tested in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require them to solve equations, interpret graphs, and apply concepts to real-world problems. Common question patterns include multiple-choice questions (MCQs), fill-in-the-blanks, and direct problem-solving scenarios, making it essential for students to be well-prepared.

Common Mistakes Students Make

Confusing the methods of substitution and elimination
Misinterpreting the slope and y-intercept in graphical representations
Overlooking the need to check solutions in original equations
Failing to convert word problems into mathematical equations accurately

FAQs

Question: What are linear equations?
Answer: Linear equations are mathematical statements that represent a straight line when graphed, typically in the form of ax + by = c.

Question: How do I solve simultaneous equations?
Answer: Simultaneous equations can be solved using methods like substitution, elimination, or graphing to find the values of the variables that satisfy both equations.

Start your journey towards mastering linear and simultaneous equations today! Solve practice MCQs and test your understanding to excel in your exams. With consistent practice, you can conquer this topic and achieve your academic goals!

Q. Find the values of x and y from the equations: 4x + 5y = 20 and 2x - y = 3. What is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

From the second equation, y = 2x - 3. Substituting into the first gives 4x + 5(2x - 3) = 20. Simplifying leads to 4x + 10x - 15 = 20, thus 14x = 35, so x = 2.5.

Correct Answer: C — 3

Q. Find the values of x and y from the equations: 4x + 5y = 20 and 2x - y = 3. What is the value of y?

A. 1
B. 2
C. 3
D. 4

Solution

From the second equation, y = 2x - 3. Substituting into the first gives 4x + 5(2x - 3) = 20. Solving leads to y = 3.

Correct Answer: C — 3

Q. Find x and y from: 8x + 2y = 34 and 3x + 5y = 29. What is the value of y?

A. 3
B. 4
C. 5
D. 6

Solution

From the first equation, 2y = 34 - 8x, so y = (34 - 8x)/2. Substituting into the second gives 3x + 5(34 - 8x)/2 = 29. Solving leads to y = 5.

Correct Answer: C — 5

Q. Find x and y from: 8x + 2y = 50 and 3x + 5y = 35. What is the value of x?

A. 4
B. 5
C. 6
D. 7

Solution

From the first equation, y = (50 - 8x)/2. Substituting into the second gives 3x + 5((50 - 8x)/2) = 35. Solving leads to x = 4.

Correct Answer: A — 4

Q. Find x and y from: 8x + 7y = 56 and 3x + 2y = 18. What is the value of x?

A. 4
B. 5
C. 6
D. 7

Solution

From the first equation, 7y = 56 - 8x. Substituting into the second gives 3x + 2(56 - 8x)/7 = 18. Solving gives x = 4.

Correct Answer: A — 4

Q. Given the equations: x + 2y = 10 and 3x - y = 5, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

From the first equation, x = 10 - 2y. Substituting into the second gives 3(10 - 2y) - y = 5. Solving leads to x = 3.

Correct Answer: D — 4

Q. Given the equations: x + 2y = 10 and 3x - y = 5, what is the value of y?

A. 1
B. 2
C. 3
D. 4

Solution

From the first equation, y = (10 - x)/2. Substituting into the second gives 3x - (10 - x)/2 = 5. Solving leads to y = 2.

Correct Answer: B — 2

Q. If 2x + 3y = 18 and 4x - y = 10, what is the value of y?

A. 2
B. 3
C. 4
D. 5

Solution

From the first equation, y = (18 - 2x)/3. Substituting into the second gives 4x - (18 - 2x)/3 = 10. Solving leads to y = 4.

Correct Answer: C — 4

Q. If 3x + 4y = 24 and 5x - 2y = 10, what is the value of y?

A. 2
B. 3
C. 4
D. 5

Solution

From the first equation, 4y = 24 - 3x. Substituting into the second gives 5x - 2(24 - 3x)/4 = 10. Solving this leads to y = 2.

Correct Answer: A — 2

Q. If 5x + 3y = 15 and 2x + 4y = 10, what is the value of y?

A. 1
B. 2
C. 3
D. 4

Solution

From the first equation, 3y = 15 - 5x, so y = (15 - 5x)/3. Substituting into the second gives 2x + 4(15 - 5x)/3 = 10. Solving leads to y = 2.

Correct Answer: B — 2

Q. If 5x + 3y = 30 and 2x + y = 12, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

From the second equation, y = 12 - 2x. Substituting into the first gives 5x + 3(12 - 2x) = 30. Solving leads to x = 3.

Correct Answer: C — 4

Q. If 5x + 3y = 30 and 2x + y = 12, what is the value of y?

A. 4
B. 5
C. 6
D. 7

Solution

From the second equation, y = 12 - 2x. Substituting into the first gives 5x + 3(12 - 2x) = 30. Solving gives y = 5.

Correct Answer: B — 5

Q. If 9x + 4y = 36 and 2x + 3y = 12, what is the value of y?

A. 2
B. 3
C. 4
D. 5

Solution

From the second equation, 3y = 12 - 2x. Substituting into the first gives 9x + 4(12 - 2x)/3 = 36. Solving gives y = 3.

Correct Answer: B — 3

Q. If 9x + 4y = 50 and 2x - 3y = -1, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

From the second equation, 2x = -1 + 3y, so x = (-1 + 3y)/2. Substituting into the first gives 9((-1 + 3y)/2) + 4y = 50. Solving leads to x = 2.

Correct Answer: A — 2

Q. Solve for x and y: 7x + 2y = 14 and 3x + 4y = 18. What is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

From the first equation, y = (14 - 7x)/2. Substituting into the second gives 3x + 4((14 - 7x)/2) = 18. Solving leads to x = 2.

Correct Answer: B — 2

Q. Solve for x and y: 7x + 2y = 34 and 3x + 4y = 18. What is the value of y?

A. 2
B. 3
C. 4
D. 5

Solution

From the first equation, 2y = 34 - 7x, so y = (34 - 7x)/2. Substituting into the second equation gives 3x + 4(34 - 7x)/2 = 18. Solving leads to y = 3.

Correct Answer: B — 3

Q. Solve the equations: 2x + 3y = 12 and x - y = 1. What is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

From the second equation, x = y + 1. Substituting into the first gives 2(y + 1) + 3y = 12. Simplifying, 2y + 2 + 3y = 12, so 5y = 10, thus y = 2. Therefore, x = 3.

Correct Answer: B — 3

Q. Solve the system: 6x + 5y = 30 and 4x - 3y = 6. What is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

From the first equation, 5y = 30 - 6x, so y = (30 - 6x)/5. Substituting into the second gives 4x - 3(30 - 6x)/5 = 6. Solving leads to x = 2.

Correct Answer: B — 2

Q. Solve the system: 6x + 5y = 45 and 4x - 3y = 1. What is the value of y?

A. 5
B. 6
C. 7
D. 8

Solution

From the first equation, 5y = 45 - 6x. Substituting into the second gives 4x - 3(45 - 6x)/5 = 1. Solving gives y = 5.

Correct Answer: A — 5

Q. Solve the system: 6x + 5y = 45 and 4x - 3y = 7. What is the value of y?

A. 5
B. 6
C. 7
D. 8

Solution

From the first equation, y = (45 - 6x)/5. Substituting into the second gives 4x - 3((45 - 6x)/5) = 7. Solving leads to y = 5.

Correct Answer: A — 5

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