Share & grow the world's knowledge!
We want to connect the people who have knowledge to the people who need it, to bring together people with different perspectives so they can understand each other better, and to empower everyone to share their knowledge.
The solution of the pair of equations x – y = 2 and x + y = 4 is:
The system of equations given is: 1. x – y = 2 .(i) 2. x + y = 4 .(ii) Add (i) and (ii): (x – y) + (x + y) = 2 + 4 ⇒ 2x = 6 ⇒ x = 3 Putting x = 3 in (i): 3 – y = 2 ⇒ y = 1
The system of equations given is:
1. x – y = 2 .(i)
2. x + y = 4 .(ii)
Add (i) and (ii):
(x – y) + (x + y) = 2 + 4
⇒ 2x = 6
⇒ x = 3
Putting x = 3 in (i):
3 – y = 2
See less⇒ y = 1
If 3x + 4y = 10 and 6x + ky = 20 have a unique solution, then the value of k must not be:
Step 1: Understanding Unique Solution Conditions • A system of two linear equations has a unique solution when the equations are linearly independent. • Linear independence means the lines represented by these equations are not parallel. Step 2: Mathematical Representation Given equations: 1. 3x + 4Read more
Step 1: Understanding Unique Solution Conditions
• A system of two linear equations has a unique solution when the equations are linearly independent.
• Linear independence means the lines represented by these equations are not parallel.
Step 2: Mathematical Representation
Given equations:
1. 3x + 4y = 10 (Equation ₁)
2. 6x + ky = 20 (Equation ₂)
Step 3: Condition for Unique Solution
For a unique solution, the coefficient matrix must have a non-zero determinant.
Coefficient matrix = [³⁄₁ ⁴⁄₁]
[⁶⁄₁ ᵏ⁄₁]
Step 4: Determinant Calculation
det = (3 * k) – (4 * 6)
= 3k – 24
Step 5: Uniqueness Condition
For unique solution, det ≠ 0
3k – 24 ≠ 0
3k ≠ 24
k ≠ 8
Step 6: Identifying Impossible k
The condition k = 8 makes the lines parallel, preventing a unique solution.
Click here for more:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
Class 6 Maths Ganita Prakash Chapter 3 MCQ?
Chapter 3 of Class 6 Maths Ganita Prakash, titled "Number Play," uses engaging activities to explore number patterns, divisibility rules, and basic operations. The MCQs in this chapter are crucial as they test students' understanding and enhance logical thinking and problem-solving skills. Solving tRead more
Chapter 3 of Class 6 Maths Ganita Prakash, titled “Number Play,” uses engaging activities to explore number patterns, divisibility rules, and basic operations. The MCQs in this chapter are crucial as they test students’ understanding and enhance logical thinking and problem-solving skills.
Solving these questions strengthens numerical ability, helps identify patterns, and applies rules creatively. This makes learning interactive and enjoyable, building a strong mathematical foundation for young learners.
Click here for more:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-6-maths-chapter-3/
Class 6 Maths Ganita Prakash Chapter 2 MCQ?
Chapter 2 of Class 6 Maths, Lines and Angles, introduces basics like parallel, intersecting, and perpendicular lines, and types of angles. It builds geometric understanding and problem-solving skills. Mastering this chapter is vital as it lays the foundation for advanced geometry, helps in spatial rRead more
Chapter 2 of Class 6 Maths, Lines and Angles, introduces basics like parallel, intersecting, and perpendicular lines, and types of angles. It builds geometric understanding and problem-solving skills.
Mastering this chapter is vital as it lays the foundation for advanced geometry, helps in spatial reasoning, and applies to real-life scenarios like construction, design, and navigation.
For more informations:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-6-maths-chapter-2/
Class 6 Maths Ganita Prakash Chapter 1 MCQ?
Chapter 1 of Class 6 Maths in Ganita Prakash introduces numbers, place values, and basic operations. The MCQs test skills in digit identification, number comparison, and arithmetic. This chapter builds a strong foundation in mathematics, fostering critical thinking and problem-solving abilities. UndRead more
Chapter 1 of Class 6 Maths in Ganita Prakash introduces numbers, place values, and basic operations. The MCQs test skills in digit identification, number comparison, and arithmetic. This chapter builds a strong foundation in mathematics, fostering critical thinking and problem-solving abilities. Understanding these basics is vital for mastering advanced concepts and excelling in future studies.
Checkout for more content:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-6-maths-chapter-1/