Grade 10 : Pair of Linear equations in two variables @2

3. Pair of Linear equations in two variables

Grade : 10

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1. For what value of k , will the following system of linear equations has no solution ?

3x + y = 1; (2k - 1) x + (k-1) y = 2k +1

2. Find the value of k for which the following system of linear equations has infinite solutions...

x + (k+1) y = 5; (k+1)x +9y = 8k -1

3. Find the values of p and q for which the following system of equations has infinite number of solutions.

4. For what value of k, will the system of equations x +2y =5, 3x +ky - 15 =0 has
i) a unique solution ? ii) no solution ?

5. Find the value of k for which each of the following systems of equations have infinitely many solution ?

i) 2x +3y = 2; (k+2)x +(2k+1)y = 2(k-1)

ii) kx +3y = 2k+1; 2(k+1)x +9y =7k+1

6. For what value of k the system of equations kx+3y=k-3; 12x +ky= k will have no solution ?

7. Find the values of a and b for which the following system of equations has infinitely many solutions ?

i) 2x + 3y-7 =0 ; (a-1)x + (a+1)y = (3a -1)

ii) (a-1)x + 3y =2; 6x+(1-2b)y =6

8. Jamila sold a table and a chair for Rs 1050, thereby making a profit of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she would have got Rs 1065. Find the cost price of each.

9. 

Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received Rs. 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs. 20 more as annual interest. How much money did she invest in each scheme?

ANSWERS