Question 1 :
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 2 :
Is x = 1, y = 7 a solution of $2x + 3y = 5$?
Question 3 :
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?
Question 4 :
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 5 :
Solve the following pair of linear equations by the elimination method and the substitution method : $x + y = 5 ~and ~2x – 3y = 4$
Question 7 :
Solve the following pair of linear equations: $px + qy = p – q ; qx – py = p + q$
Question 8 :
Solve the pair of equations: $\frac{2}{x} + \frac{3}{y} = 13 ; \frac{5}{x} - \frac{4}{y} = -2$
Question 9 : <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 10 :
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
Question 11 :
Solve the following pair of linear equations by the substitution method : $0.2x + 0.3y = 1.3 ; 0.4x + 0.5y = 2.3$
Question 12 :
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 14 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $3x + 2y = 5 ; 2x – 3y = 7$
Question 15 : <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 16 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $5x – 3y = 11 ; – 10x + 6y = –22$
Question 17 :
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 18 :
Solve the following pair of linear equations by the substitution method : $\sqrt{2}x + \sqrt{3}y =0 ; \sqrt{3}x - \sqrt{8}y =0$
Question 19 :
Is the pair of equations x + 2y – 3 = 0 and 6y + 3x – 9 = 0 consistent?
Question 20 :
Solve the following pair of linear equations by the substitution and cross-multiplication methods : $8x + 5y = 9 ; 3x + 2y = 4$
Question 21 :
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 22 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $2x + y = 5 ; 3x + 2y = 8$
Question 23 :
Use elimination method to find all possible solutions of the following pair of linear equations :$2x + 3y =8 , 4x + 6y =7$
Question 24 :
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 25 :
Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis.
Question 26 :
The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number.
Question 27 :
A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs. 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs. 1180 as hostel charges. Find the fixed charges and the cost of food per day.
Question 28 :
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 29 :
An equation which can be put in the form ax + by + c = 0,where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables x and y. TRUE or FALSE?
Question 30 :
Champa went to a ‘Sale’ to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, “The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”. Find how many pants and skirts Champa bought, graphically.
