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Pair of Liner Equation in Two Variable

For which value(s) of k will the pair of equations

kx + 3y = k – 3

12x + ky = k

have no solution?

Pair of Liner Equation in Two Variable

For which value(s) of λ , do the pair of linear equations

 λx + y = λ²  and x +  λy = 1    have

(i) no solution?

(ii) infinitely many solutions?

(iii) a unique solution?

Pair of Liner Equation in Two Variable

Draw the graphs of the pair of linear equations x – y + 2 = 0 and 4x – y – 4 = 0. Calculate the area of the triangle formed by the lines so drawn and the x-axis.

Pair of Liner Equation in Two Variable

For which values of p and q, will the following pair of linear equations have infinitely many solutions?

Pair of Liner Equation in Two Variable

For all real values of c, the pair of equations

x – 2y = 8

5x – 10y = c

have a unique solution. Justify whether it is true or false.

Pair of Liner Equation in Two Variable

 Is the pair of equations  x + 2y – 3 = 0 and 6y + 3x – 9 = 0 consistent? Justify your answer.

Pair of Liner Equation in Two Variable

 Do the equations 4x + 3y – 1 = 5 and 12x + 9y = 15 represent a pair of coincident lines? Justify your answer.

Pair of Liner Equation in Two Variable

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

(A) 4 and 24 (B) 5 and 30
(C) 6 and 36 (D) 3 and 24

Pair of Liner Equation in Two Variable

Aruna has only Re 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75, then the number of Re 1 and Rs 2 coins are, respectively
(A) 35 and 15 (B) 35 and 20
(C) 15 and 35 (D) 25 and 25

Pair of Liner Equation in Two Variable

If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are, respectively
(A) 3 and 5 (B) 5 and 3
(C) 3 and 1 (D) –1 and –3