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