Linear Equations In Two Variables - 2 - Free MCQ Practice Test with solutions,

- 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.

Given Equation:

The equation to consider is x − 2y = 4.

Evaluating Each Option:

1. Option a) (0, 2)
   Substitute: Let’s plug in x = 0 and y = 2 into the equation.
   Calculation: 0 − 2 × 2 = 0 − 4 = −4
   Check: −4 does not equal 4.
   Conclusion: This point does not satisfy the equation.
2. Option b) (4, 0)
   Substitute: Let’s plug in x = 4 and y = 0 into the equation.
   Calculation: 4 − 2 × 0 = 4 − 0 = 4
   Check: 4 equals 4.
   Conclusion: This point does satisfy the equation.
3. Option c) (2, 0)
   Substitute: Let’s plug in x = 2 and y = 0 into the equation.
   Calculation: 2 − 2 × 0 = 2 − 0 = 2
   Check: 2 does not equal 4.
   Conclusion: This point does not satisfy the equation.
4. Option d) (1, 1)
   Substitute: Let’s plug in x = 1 and y = 1 into the equation.
   Calculation: 1 − 2 × 1 = 1 − 2 = −1
   Check: −1 does not equal 4.
   Conclusion: This point does not satisfy the equation.

Final Conclusion:
After evaluating all the options, only Option b) (4, 0) satisfies the equation x − 2y = 4.

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.

To find which pair is a solution to the equation 4x + 3y = 10, substitute each pair into the equation:

(1, 2): Substitute to get 4(1)+3(2)
= 4+6
= 10.
This pair works.

(0, 4): Substitute to get 4(0)+3(4)
= 0+12
= 12.
This pair does not work.

(-1, 6): Substitute to get 4(-1)+3(6)
= -4+18
= 14.
This pair does not work.

(2, 0): Substitute to get 4(2)+3(0)
= 8+0
= 8.
This pair does not work.

The solution is (1, 2) because it satisfies the equation.

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.