Linear Equations in Two Variables — Flashcards
Karnataka Board · Class 9 · Mathematics
20 flashcards for Linear Equations in Two Variables (Karnataka Board Class 9 Mathematics) to test yourself on key terms and facts.
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Solve for y when x = 3 in the equation: 2x + 3y = 12
Answer
Step 1: Substitute x = 3 into the equation: 2(3) + 3y = 12 Step 2: Simplify: 6 + 3y = 12 Step 3: Subtract 6 from both sides: 3y = 6 Step 4: Divide by 3: y = 2 Answer: When x = 3, y = 2. Solution: (3, …
Write the equation x - 4 = √3y in standard form ax + by + c = 0
Answer
Step 1: Move all terms to one side: x - 4 - √3y = 0 Step 2: Rearrange in standard form: x - √3y - 4 = 0 Step 3: Identify coefficients: a = 1, b = -√3, c = -4 Answer: x - √3y - 4 = 0 where a = 1, b = -…
Find three different solutions for the equation: x + 2y = 8
Answer
Method: Choose values for one variable and solve for the other. Solution 1: Let x = 0 → 0 + 2y = 8 → y = 4. Point: (0, 4) Solution 2: Let y = 0 → x + 2(0) = 8 → x = 8. Point: (8, 0) Solution 3: Let x …
Check if (4, -1) is a solution of 3x - 2y = 14
Answer
Step 1: Substitute x = 4 and y = -1 into the equation Step 2: 3(4) - 2(-1) = 12 + 2 = 14 Step 3: Compare with right side: 14 = 14 ✓ Step 4: Since both sides are equal, the point satisfies the equation…
A notebook costs twice as much as a pen. If notebook costs ₹x and pen costs ₹y, write the linear equation.
Answer
Step 1: Understand the relationship: notebook = 2 × pen Step 2: Express in terms of variables: x = 2y Step 3: Convert to standard form: x - 2y = 0 Step 4: Add zero constant: x - 2y + 0 = 0 Answer: x =…
Find the value of k if (2, 1) is a solution of 2x + 3y = k
Answer
Step 1: Point (2, 1) means x = 2 and y = 1 Step 2: Substitute into the equation: 2(2) + 3(1) = k Step 3: Calculate: 4 + 3 = k Step 4: Simplify: k = 7 Verification: 2(2) + 3(1) = 4 + 3 = 7 ✓ Answer: k …
Solve: 4x + 3y = 12 when y = 0
Answer
Step 1: Substitute y = 0 into the equation: 4x + 3(0) = 12 Step 2: Simplify: 4x + 0 = 12 Step 3: Simplify further: 4x = 12 Step 4: Divide by 4: x = 3 Step 5: Write as ordered pair: (3, 0) Answer: When…
Express y = 2 as a linear equation in two variables in standard form
Answer
Step 1: Understand that x can have any value while y = 2 Step 2: Write with x coefficient: 0·x + 1·y = 2 Step 3: Convert to standard form: 0x + 1y - 2 = 0 Step 4: Identify coefficients: a = 0, b = 1, …
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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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