Question 1 : State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $x – 3y – 7 = 0 ; 3x – 3y – 15 = 0$

Question 2 : Meena went to a bank to withdraw Rs. 2000. She asked the cashier to give her Rs. 50 and Rs. 100 notes only. Meena got 25 notes in all. Find how many notes of Rs. 50 and Rs. 100 she received.

Question 3 : Is x = 1, y = 7 a solution of $2x + 3y = 5$?

Question 4 : The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

Question 5 : Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2 ; \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = -1$.

Question 6 : Let a pair of linear equations in two variables be $a_{1}x+b_{1}y+c_{1}=0$ and $a_{2}x+b_{2}y+c_{2}=0$. If $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$, then the pair of linear equations is _______.

Question 7 : Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Question 8 : Solve the following pair of linear equations: 21x + 47y = 110 and 47x + 21y = 162.

Question 9 : Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{6}{x-1} - \frac{3}{y-2} = 1 ; \frac{5}{x-1} + \frac{1}{y-2} = 2$

Question 10 : The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. Which of these represent the situation algebraically?

Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdc273b230584979a30.png' /> In the above fig, the lines represents ____________ lines.

Question 12 : Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions: $5x – 8y + 1 =0 ; 3x - \frac{24}{5}y + \frac{3}{5} = 0$

Question 13 : Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4} ; \frac{1}{2(3x+y)} - \frac{1}{2(3x-y)} = \frac{-1}{8}$.

Question 16 : Solve the following pair of linear equations by the substitution method : $\frac{3x}{2} - \frac{5y}{3} = -2 ; \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

Question 17 : Solve the following pair of equations by reducing them to a pair of linear equations : $6x + 3y = 6xy ; 2x + 4y = 5xy$.

Question 18 : Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

Question 19 : Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Which of these represent this situation algebraically?

Question 20 : Solve the following pair of equations by substitution method: $s-7t+42=0 ; s-3t=6$