#### Class nine Maths Chapter 4 additional Q-A

**Chapter 4: Linear Equations in Two Variables ( Additional Questions-Answers)**

**Very Short Answer Type Questions: [1 Mark] **

**1. Age of ‘x’ exceeds the age of ‘y’ by 7 years. Write this statement as a linear equation. **

**Sol. **According to the given statement,

x = y + 7

⇒ x – y – 7 = 0

**2. What is the general form of a linear equation in two variables?**

**Sol. **An equation which can be put in the form ax + by + c = 0, where a, b, c are real numbers and a, b _ 0 is called a linear equation in two variables.

**3. **Which of the following is a linear equation in one variable?

2x = y, y2 = 3y + 5 , 4x – y = 5, 3t + 5 = 9t – 7

**Sol. **2x = y and 4x – y = 5 is a form of a linear equation in two variable and y2 = 3y + 5 is a form of a quadratic equation.

And, 3t + 5 = 9t – 7

⇒ 3t – 9t + 5 +7 = 0

⇒ –6t + 12 = 0 ⇒ 6t = 12 is a form of linear equation in one variable.

**4. Which of the following is not a form of linear equation in two variables ? **

ax + by + c = 0, ax + 0y + b = 0,

0x + ay + b = 0, 0x + 0y + 5 = 0

**Sol. **0x + 0y + 5 = 0 is not a form of linear equation in two variables because it is reduced to 5 = 0, which is not true.

**5. Which of the following is not a linear equation? **

ax + by + c = 0, 0x + 0y + c = 0,

bx + ay + c = 0, ax + 0y + c = 0

**Sol. **Equation 0x + 0y + c = 0 is not a form of linear equation in two variables because it is reduced to c = 0, which is not true.

**6. For the equation x – 2y = 4, check which of the following is a solution? **

**(0, 2), (2, 0), (4, 0), (1, 1) **

**Sol. **Substituting x = 4 and y = 0 in LHS of x –
2y = 4, we get 4 – 2 × 0 = 4 =
RHS.

Hence, (4, 0) is solution of x – 2y = 4 .

**7. If (2, 0) is a solution of linear equation 2x + 3y = k, then find the value of k. **

**Sol. **On putting x = 2, y = 0 in equation 2x + 3 y = k, we get 2 × 2 + 3 × 0

= k ⇒ k = 4

**8. How many solutions does y = 2x + 3 have: **

**Sol. **Infinitely many solutions. It is because a linear equation in two variables has infinitely many solutions. We keep changing the value of x and solve the linear equation for the corresponding value of y.

**9. Which of the following is a solution of the equation –5x + 2y = 14? **

x = 5, y = 1; x = 0, y = – 7; x = –2, y = 2;

x = 1, y = – 3

**Sol. **For x = – 2, y = 2,

LHS = –5 × (–2) + 2 × 2 = 10 + 4 = 14 = RHS

**10. Which of the following is not a solution of the equation 2x + y = 7? **

**(1, 5); (3, 1); (1, 3); (0, 7) **

**Sol. **When
x = 1, y = 3, 2 × 1 + 3 = 5

⇒ LHS ≠ RHS Therefore, (1, 3) is not a solution.

**11. How many solutions does a linear equation in two variables have? **

**Sol. **A linear equation in two
variables has infinitely many solutions.

**12. How many linear equations in x and y can be satisfied by x = 1 and y = 2? **

**Sol. **There are infinitely many equations which are satisfied by x