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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.
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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.
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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.
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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.
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What is a museum? How does it help in preserving history and traditions?
A museum is an institution where historical cultural and scientific objects are preserved and displayed. It plays a vital role in preserving history and traditions by showcasing artefacts manuscripts paintings and sculptures. Museums help people understand past civilizations traditions and lifestyleRead more
A museum is an institution where historical cultural and scientific objects are preserved and displayed. It plays a vital role in preserving history and traditions by showcasing artefacts manuscripts paintings and sculptures. Museums help people understand past civilizations traditions and lifestyles by displaying objects from different eras. They protect valuable items from damage and ensure that future generations can learn from them.
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