Question 1 :
Solve the following pair of linear equations: $px + qy = p – q ; qx – py = p + q$
Question 2 :
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 3 :
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 4 : <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 5 :
The pair of equations 5x – 15y = 8 and $3x-9y=\frac{24}{5}$ has __________.
Question 6 :
Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Question 7 :
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 8 :
The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
Question 9 :
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are parallel lines.
Question 10 :
Two linear equations are in the same two variables x and y. Equations like these are called a pair of linear equations in one variable. TRUE or FALSE?
Question 11 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{7x-2y}{xy} = 5 ; \frac{8x+7y}{xy} = 15$.
Question 12 :
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 13 :
Akhila goes to a fair with Rs. 20 and wants to have rides on the Giant Wheel and play Hoopla. The number of times she played hoopla is half the number of times she went on giant wheel. Which of these represent this situation algebraically ?
Question 14 :
Use elimination method to find all possible solutions of the following pair of linear equations :$2x + 3y =8 , 4x + 6y =7$
Question 15 :
10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. Find the solution graphically.
Question 16 :
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ___________.
Question 17 :
For which values of a and b does the following pair of linear equations have an infinite number of solutions? $2x + 3y = 7 ; (a – b) x + (a + b) y = 3a + b – 2$
Question 18 :
Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3, 2x – 3y = 2 and x + 2y = 8.
Question 19 :
Solve the following pair of linear equations by the substitution method : $s - t = 3 ; \frac{s}{3} + \frac{t}{2} = 6$
Question 20 :
Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Question 21 :
What is/ are the algebraic method/ methods that can solve a pair of linear equations?
Question 22 :
Do the equations 4x + 3y – 1 = 5 and 12x + 9y = 15 represent a pair of coincident lines?
Question 23 :
Solve the following pair of linear equations: $152x – 378y = – 74 ; –378x + 152y = – 604$
Question 24 :
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 25 :
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Question 26 :
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 27 :
Solve the following pair of linear equations by the elimination method and the substitution method : $x + y = 5 ~and ~2x – 3y = 4$
Question 28 :
The cost of 5 oranges and 3 apples is Rs. 35 and the cost of 2 oranges and 4 apples is Rs. 28. Let us find the cost of an orange and an apple.
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdc273b230584979a2f.png' />
In the above fig, the lines represents ____________ lines.
Question 30 :
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are coincident lines.
Question 31 :
5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen, graphically.
Question 32 :
In case of infinitely many solutions, the pair of linear equations is said to be __________.
Question 33 :
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 34 :
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 35 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{1}{2x} + \frac{1}{3y} = 2 ; \frac{1}{3x} + \frac{1}{2y} = \frac{13}{6}$.
Question 36 :
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 37 :
From a bus stand in Bangalore , if we buy 2 tickets to Malleswaram and 3 tickets to Yeshwanthpur, the total cost is Rs. 46; but if we buy 3 tickets to Malleswaram and 5 tickets to Yeshwanthpur the total cost is Rs. 74. Find the fares from the bus stand to Malleswaram, and to Yeshwanthpur.
Question 38 :
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 39 :
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 40 :
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.
Question 42 :
Solve the pair of equations: $\frac{2}{x} + \frac{3}{y} = 13 ; \frac{5}{x} - \frac{4}{y} = -2$
Question 43 :
The cost of 2 pencils and 3 erasers is Rs. 9 and the cost of 4 pencils and 6 erasers is Rs. 18. Find the cost of each pencil and each eraser.
Question 44 :
Solve the following pair of equations by reducing them to a pair of linear equations : $6x + 3y = 6xy ; 2x + 4y = 5xy$.
Question 45 :
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Question 46 :
Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
Question 47 :
A pair of linear equations is inconsistent, if it has ___________.
Question 48 :
A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.
Question 49 :
Every solution of the equation is a _________ on the line representing it.
Question 50 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $x – 3y – 3 = 0 ; 3x – 9y – 2 = 0$
