NCERT Solutions Class 9 Maths Chapter 4 — Linear Equations in Two Variables

Solution:

Step 1: A linear equation in two variables can be written in the form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero.

Step 2: The degree of each variable (x and y) must be 1. Option A, 2x + 3y = 5 (or 2x + 3y - 5 = 0), fits this definition as both x and y have a degree of 1.

Step 3: Options B (x² + y = 7) has x with degree 2, option C (xy = 4) has a product of variables making it non-linear, and option D (3x = 9) is a linear equation in only one variable.

Solution:

Step 1: The given equation is 3x = 5y - 8.

Step 2: To express it in the standard form ax + by + c = 0, we need to move all terms to the left side of the equation.

Step 3: Subtract 5y and add 8 to both sides: 3x - 5y + 8 = 0.

Step 4: Comparing this with ax + by + c = 0, we find a = 3, b = -5, and c = 8.

Solution:

Step 1: A point (x, y) is a solution to an equation if, when substituted into the equation, it makes the equation true.

Step 2: Let's check option A: (1, 4) => 2(1) + 4 = 2 + 4 = 6 ≠ 7.

Step 3: Let's check option B: (3, 2) => 2(3) + 2 = 6 + 2 = 8 ≠ 7.

Step 4: Let's check option C: (2, 3) => 2(2) + 3 = 4 + 3 = 7. This satisfies the equation.

Step 5: Let's check option D: (0, 7) => 2(0) + 7 = 0 + 7 = 7. This also satisfies the equation. Oh wait, I need to pick only ONE correct answer. I will adjust the options to ensure only one is correct. Let me re-evaluate.

Solution:

Step 1: A point (x, y) is a solution to an equation if, when substituted into the equation, it makes the equation true.

Step 2: For option A (1, 4): 2(1) + 4 = 2 + 4 = 6 ≠ 7.

Step 3: For option B (3, 2): 2(3) + 2 = 6 + 2 = 8 ≠ 7.

Step 4: For option C (2, 3): 2(2) + 3 = 4 + 3 = 7. This is true, so (2, 3) is a solution.

Step 5: For option D (4, -1): 2(4) + (-1) = 8 - 1 = 7. This is also true. Oh no, I made the same mistake again. I need to make sure only ONE option is correct. Let me adjust the options once more.

Solution:

Step 1: A point (x, y) is a solution to an equation if, when substituted into the equation, it makes the equation true.

Step 2: For option A (1, 4): 2(1) + 4 = 2 + 4 = 6 ≠ 7.

Step 3: For option B (3, 2): 2(3) + 2 = 6 + 2 = 8 ≠ 7.

Step 4: For option C (2, 3): 2(2) + 3 = 4 + 3 = 7. This is true, so (2, 3) is a solution.

Step 5: For option D (4, 0): 2(4) + 0 = 8 + 0 = 8 ≠ 7.