Linear Equations in Two Variables — Flashcards
Gujarat Board · Class 9 · Mathematics
24 flashcards for Linear Equations in Two Variables (Gujarat Board Class 9 Mathematics) to test yourself on key terms and facts.
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Identify which of the following is a linear equation in two variables: (i) 2x + 3y = 5, (ii) x² + y = 4, (iii) 3x + 2y + z = 6
Answer
Answer: (i) 2x + 3y = 5 is a linear equation in two variables. Step 1: Check if equation is in form ax + by + c = 0 where a and b are not both zero. Step 2: For (i): 2x + 3y - 5 = 0. This has variabl…
Express 3y = 2x - 7 in the form ax + by + c = 0 and identify a, b, and c.
Answer
Step 1: Start with 3y = 2x - 7 Step 2: Move all terms to one side: 2x - 3y - 7 = 0 (or -2x + 3y + 7 = 0) Step 3: Rearrange in standard form: 2x - 3y - 7 = 0 Step 4: Compare with ax + by + c = 0 Answe…
Check if (2, 1) is a solution of the equation 2x + y = 5. Show your working.
Answer
Step 1: Substitute x = 2 and y = 1 into the equation 2x + y = 5 Step 2: Left side = 2(2) + 1 = 4 + 1 = 5 Step 3: Right side = 5 Step 4: Since Left side = Right side (5 = 5), the equation is satisfied …
Find the value of k if (1, 2) is a solution of kx + 3y = 7.
Answer
Step 1: Substitute x = 1 and y = 2 into kx + 3y = 7 Step 2: k(1) + 3(2) = 7 Step 3: k + 6 = 7 Step 4: Solve for k by subtracting 6 from both sides Step 5: k = 7 - 6 = 1 Answer: k = 1 Verification: S…
Find three different solutions of the equation x + 2y = 6.
Answer
Method: Choose values for x and find corresponding y values. Solution 1: Let x = 0 Step 1: 0 + 2y = 6 Step 2: 2y = 6 Step 3: y = 3 Solution: (0, 3) ✓ Solution 2: Let x = 2 Step 1: 2 + 2y = 6 Step 2:…
Why does a linear equation in two variables have infinitely many solutions? Explain with an example.
Answer
Reason: A linear equation in two variables has one equation but two unknowns. This underdetermined system allows infinite solutions. Example: Consider 2x + y = 5 Explanation: - We can choose ANY val…
Write a linear equation in two variables for: 'The cost of a notebook is twice the cost of a pen.' (Notebook = x, Pen = y)
Answer
Step 1: Identify the relationship: Cost of notebook = 2 × Cost of pen Step 2: Use variables: x = cost of notebook, y = cost of pen Step 3: Translate to equation: x = 2y Step 4: Rearrange to standard f…
Check which of these pairs are solutions of 3x - y = 9: (i) (3, 0), (ii) (2, 3), (iii) (4, 3), (iv) (0, 9)
Answer
We substitute each pair into 3x - y = 9: (i) (3, 0): 3(3) - 0 = 9 - 0 = 9 ✓ SOLUTION (ii) (2, 3): 3(2) - 3 = 6 - 3 = 3 ≠ 9 ✗ NOT a solution (iii) (4, 3): 3(4) - 3 = 12 - 3 = 9 ✓ SOLUTION (iv) (0, …
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