Test: Linear Equations In Two Variables - 2 - Class 9 MCQ

- A linear equation in two variables has infinitely many solutions, corresponding to all the points on the line.
- Therefore, the correct answer is:
- C: It has infinitely many solutions.

Correct Answer: B - (2,3)

x = 2 and y = 3into the equation:

2(2) + 3 = 4 + 3 = 7, which is true.

Answer: D) (4, 1)
Substituting x = 4 and y = 1 into the equation:
4 = 4(1), which is true.

Answer: B) (2, 0)
Substituting x = 2 and y = 0 into the equation:
2 - 2(0) = 2, which is not equal to 4. Thus, the correct answer is B) (2, 0).

Substituting x = 2 and y = 1 into the equation:
2(2) + 3(1) = 4 + 3 = 7, so k = 7.

Substituting 
a) (2, 3) into the equation 3x + 2y = 12  
3(2) + 2(3) = 6 + 6 = 12,
which satisfies the equation. Therefore, the correct solution is option b) (2, 3).

Answer: A) (2, 4)
Explanation: Substituting x = 2 and y = 4 into the equation:
4(2) − 4 = 8 − 4 = 8, which is true.

Answer: D) x + y = 2x + 2y

Explanation: Simplifying x + y = 2x + 2y, we get:
x + y - 2x - 2y = 0 or -x - y = 0 or x + y = 0, which is a contradiction.
Hence, this equation has no solution.

To determine which pair (x, y) is a solution to the equation 3x − 2y = 7, we substitute each pair into the equation and check if it satisfies the equation.

1. Option A: (1, −2)
   Substituting: 3(1) − 2(−2) = 3 + 4 = 7 (satisfies the equation)

2. Option B: (−2, 1)
   Substituting: 3(−2) − 2(1) = −6 − 2 = −8 (does not satisfy the equation)

3. Option C: (5, 1)
   Substituting: 3(5) − 2(1) = 15 − 2 = 13 (does not satisfy the equation)

4. Option D: (1, 5)
   Substituting: 3(1) − 2(5) = 3 − 10 = −7 (does not satisfy the equation)

The correct answer is:
Option A: (1, −2)

The correct answer is C: 2x – 5y = 0.
- A linear equation in two variables can be written in the form ( ax + by = c ), where ( a ), ( b ), and ( c ) are constants.
- Option C: ( 2x - 5y = 0 ) fits the form ( ax + by = c ), making it linear.