Linear Equations in Two variables

Answer

Step 1: Move all terms to one side → 3x + 2y - 9 = 0. Step 2: Identify coefficients → a = 3, b = 2, c = -9. Answer: 3x + 2y - 9 = 0 with a = 3, b = 2, c = -9

Answer

Method: Choose x values, find corresponding y values. Step 1: x = 0 → 2(0) + y = 5 → y = 5 → (0,5). Step 2: x = 1 → 2(1) + y = 5 → y = 3 → (1,3). Step 3: x = 2 → 2(2) + y = 5 → y = 1 → (2,1). Answer:

Answer

Step 1: Substitute x = 3, y = 2 → 4(3) - 3(2) = 12 - 6 = 6. Step 2: Compare with RHS → 6 = 6 ✓. Step 3: Since LHS = RHS, the point satisfies the equation. Answer: Yes, (3,2) is a solution

Answer

Step 1: Substitute x = 2, y = 1 → 3(2) + k(1) = 8. Step 2: Simplify → 6 + k = 8. Step 3: Solve for k → k = 8 - 6 = 2. Step 4: Verify → 3(2) + 2(1) = 6 + 2 = 8 ✓. Answer: k = 2

Answer

Step 1: Let the two numbers be x and y. Step 2: According to given condition → x + y = 15. Step 3: Write in standard form → x + y - 15 = 0. Answer: x + y = 15 or x + y - 15 = 0

Answer

Step 1: When x = 0 → 0 + y = 4 → y = 4 → Point A(0,4). Step 2: When y = 0 → x + 0 = 4 → x = 4 → Point B(4,0). Step 3: Plot points A(0,4) and B(4,0) on graph paper. Step 4: Draw straight line through t

Answer

Step 1: Substitute x = 3 in equation → 2(3) - 3y = 6. Step 2: Simplify → 6 - 3y = 6. Step 3: Solve for y → -3y = 6 - 6 = 0 → y = 0. Step 4: Verify → 2(3) - 3(0) = 6 - 0 = 6 ✓. Answer: y = 0

Answer

Step 1: Multiply entire equation by LCM of denominators (2,3) = 6. Step 2: 6 × (x/2 + y/3) = 6 × 5 → 3x + 2y = 30. Step 3: Move to standard form → 3x + 2y - 30 = 0. Answer: 3x + 2y - 30 = 0