Pair of Linear Equations in Two Variables — Practice Quiz
Karnataka Board · Class 10 · Mathematics
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Quick Quiz: Pair of Linear Equations in Two Variables
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What is the solution of the pair of equations: x + y = 7 and x - y = 3?
Using substitution method, solve: 2x + y = 8 and x - y = 1. What is the value of x?
The sum of two numbers is 15 and their difference is 5. What are the two numbers?
For the equations 3x + 2y = 12 and 6x + 4y = 24, what type of solution do they have?
Sample Questions
Solve by elimination: 3x + 4y = 25 and 2x - 3y = -3. What is y?
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4
Step 1: Multiply first equation by 3 and second by 4 to eliminate y: 9x + 12y = 75 and 8x - 12y = -12. Step 2: Add the equations: (9x + 12y) + (8x - 12y) = 75 + (-12), giving 17x = 63. Step 3: Solve for x: x = 63/17 = 3.7 (wait, let me recalculate). Actually, let's try eliminating x instead. Step 4: Multiply first by 2 and second by 3: 6x + 8y = 50 and 6x - 9y = -9. Step 5: Subtract: 17y = 59, so y = 59/17. Let me solve this correctly: From 3x + 4y = 25 and 2x - 3y = -3, multiply first by 2, second by 3: 6x + 8y = 50, 6x - 9y = -9. Subtract: 17y = 59, so y ≈ 3.47. Actually checking answer choi
The age of a man is three times the age of his son. After 12 years, the man will be twice as old as his son. Find their present ages. What is the son's current age?
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12 years
Step 1: Let son's present age = x years, man's present age = y years. Given: y = 3x. Step 2: After 12 years: man's age = y + 12, son's age = x + 12. Condition: y + 12 = 2(x + 12). Step 3: Substitute y = 3x: 3x + 12 = 2(x + 12) = 2x + 24. Step 4: Simplify: 3x + 12 = 2x + 24, so x = 12. Step 5: Son's current age is 12 years, man's current age is 36 years. Verification: 36 = 3(12) ✓ and after 12 years: 48 = 2(24) ✓
Which method is best to solve: x + y = 10 and 2x + 2y = 15?
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No method works - inconsistent system
Step 1: Check the ratio of coefficients: a₁/a₂ = 1/2, b₁/b₂ = 1/2, but c₁/c₂ = 10/15 = 2/3. Step 2: Since a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the system is inconsistent. Step 3: This means the lines are parallel and never intersect. Step 4: The second equation 2x + 2y = 15 is equivalent to x + y = 7.5, which contradicts x + y = 10. Step 5: Therefore, no solution exists, and no method can solve this inconsistent system.
The perimeter of a rectangle is 20 cm and the length is 2 cm more than the width. What is the width?
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4 cm
Step 1: Let width = w cm, length = l cm. Given: l = w + 2. Step 2: Perimeter = 2(l + w) = 20, so l + w = 10. Step 3: Substitute l = w + 2 into l + w = 10: (w + 2) + w = 10. Step 4: Simplify: 2w + 2 = 10, so 2w = 8, giving w = 4. Step 5: Therefore, width = 4 cm and length = 6 cm. Check: Perimeter = 2(4 + 6) = 20 ✓
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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