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# 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

x = 1 and y = 2.
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