NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 3: Pair of Linear Equations in Two Variables

Exercise 3.1

1. Graphically, the pair of equations
6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are

2. The pair of equations \(x + 2y + 5 = 0\) and \(-3x - 6y + 1 = 0\) have

3. If a pair of linear equations is consistent, then the lines will be

4. The pair of equations \(y = 0\) and \(y = -7\) has

5. The pair of equations \(x = a\) and \(y = b\) graphically represents lines which are

6. For what value of \(k\), do the equations \(3x - y + 8 = 0\) and \(6x - ky = -16\) represent coincident lines?

7. If the lines given by \(3x + 2ky = 2\) and \(2x + 5y + 1 = 0\) are parallel, then the value of \(k\) is

8. The value of \(c\) for which the pair of equations \(cx - y = 2\) and \(6x - 2y = 3\) will have infinitely many solutions is

9. One equation of a pair of dependent linear equations is \(-5x + 7y = 2\). The second equation can be

10. A pair of linear equations which has a unique solution \(x = 2\), \(y = -3\) is

11. If \(x = a\), \(y = b\) is the solution of \(x - y = 2\) and \(x + y = 4\), then \(a\), \(b\) are, respectively

12. Aruna has only Re 1 and Rs 2 coins with her. If the total number of coins is 50 and the total amount is Rs 75, then the number of Re 1 and Rs 2 coins are, respectively

13. The father’s age is six times his son’s age. Four years hence, the father’s age will be four times his son’s age. The present ages, in years, of the son and the father are, respectively