Question 1 :
In case of infinitely many solutions, the pair of linear equations is said to be __________.

Question 2 :
Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates ofthe vertices of the triangle formed by these lines and the y axis.

Question 3 :
A pair of linear equations which has no solution, is called an __________________ pair of linear equations.

Question 4 :
If the lines are represented by the equation $a_1x + b_1y + c_1 =0$ and $a_2x + b_2y + c_2 =0$, then the lines are coinciding when _____________.

Question 5 :
Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3, 2x – 3y = 2 and x + 2y = 8.

Question 6 :
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water.

Question 7 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $x – 3y – 3 = 0 ; 3x – 9y – 2 = 0$

Question 8 :
What is/ are the algebraic method/ methods that can solve a pair of linear equations?

Question 9 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b5c273b230584979988.png' /> In the above given graph 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.

Question 10 :
Solve the following pair of linear equations by the elimination method and the substitution method : $\frac{x}{2}+\frac{2y}{3}=-1 ~and~ x-\frac{y}{3}=3$

Question 11 :
Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $2x – 2y – 2 = 0 , 4x – 4y – 5 = 0$

Question 12 :
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 13 :
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Question 14 :
From the graphs of the equations x = 3, x = 5 and 2x – y – 4 = 0, find the area of the quadrilateral formed by the lines and the x–axis.

Question 15 :
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 16 :
A fraction becomes $\frac{1}{3}$ when 1 is subtracted from the numerator and it becomes $\frac{1}{4}$ when 8 is added to its denominator. Find the fraction.

Question 17 :
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 18 :
The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pencil box.

Question 19 :
A train covered a certain distance at a uniform speed. If the train would have been10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

Question 20 :
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.