Linear Equations in two Variables — Important Questions

(2, 3), (0, 5), (5, 0), (-1, 6)

To check if a point is a solution, substitute the x and y values into the equation. For (2, 3): 2 + 3 = 5 ✓. For (0, 5): 0 + 5 = 5 ✓. For (1, 3): 1 + 3 = 4 ≠ 5 ✗. For (5, 0): 5 + 0 = 5 ✓. For (-1, 6): -1 + 6 = 5 ✓.

2x + 3y = 5, x - y = 0, 3y = 7

2x + 3y = 5 can be written as 2x + 3y - 5 = 0. x - y = 0 is already in the required form. 3y = 7 can be written as 0x + 3y - 7 = 0. However, x² + y = 1 contains x², so it's not linear and cannot be written in the required form.

False

The point (0, 0) is not always a solution to linear equations in two variables. For example, in the equation x + y = 5, substituting (0, 0) gives 0 + 0 = 0, which is not equal to 5. The point (0, 0) is only a solution when the constant term c = 0 in the equation ax + by + c = 0.

2

If (3, 4) is a solution to 2x - y = k, then substituting x = 3 and y = 4: 2(3) - 4 = k, which gives 6 - 4 = 2. Therefore, k = 2.