Question 1 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bde273b230584979a32.JPG' />
In the above fig, ABCD is a cyclic quadrilateral. Find the values of x and y.
Question 2 :
Do the equations 4x + 3y – 1 = 5 and 12x + 9y = 15 represent a pair of coincident lines?
Question 3 :
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: $\frac{4}{3}x + 2y = 8 ; 2x + 3y = 12$
Question 4 :
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 5 :
Every solution of the equation is a _________ on the line representing it.
Question 6 :
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 7 :
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Question 9 :
A fraction becomes $\frac{9}{11}$, if 2 is added to both the numerator and the denominator.If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$. Find the fraction.
Question 10 :
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 11 :
The coach of a cricket team buys 3 bats and 6 balls for Rs. 3900. Later, she buys another bat and 3 more balls of the same kind for Rs. 1300. Which of these represent this situation algebraically?
Question 12 :
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 13 :
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 14 :
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 15 :
The difference between two numbers is 26 and one number is three times the other. Find them.
Question 16 :
Solve the following pair of equations by substitution method: $7x – 15y =2 ; x + 2y =3$
Question 17 :
Solve the following pair of linear equations by the substitution method : $x + y = 14 ; x - y = 4$
Question 18 :
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 19 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $2x + y = 5 ; 3x + 2y = 8$
Question 20 :
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 $\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$, then the pair of linear equations is _______.
Question 21 :
Is it true to say that the pair of equations – x + 2y + 2 = 0 and $\frac{1}{2}x-\frac{1}{4}y-1=0$ has a unique solution?
Question 22 :
Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $x – y = 8 , 3x – 3y = 16$
Question 23 :
The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later, she buys 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.
Question 24 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdb273b230584979a2e.png' />
In the above fig, the lines represents ____________ lines.
Question 25 :
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 $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, then the pair of linear equations is _______.
Question 26 :
Solve the following pair of linear equations: $px + qy = p – q ; qx – py = p + q$
Question 27 :
One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?
Question 28 :
Is the pair of equations x + 2y – 3 = 0 and 6y + 3x – 9 = 0 consistent?
Question 29 :
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 30 :
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 parallel when _____________.
Question 31 :
In the following pair of equations: 2x + y = 6 and 2x – y + 2 = 1, find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.
Question 32 :
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 33 :
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 intersect at a point, are parallel or coincident: $5x – 4y + 8 = 0 ; 7x + 6y – 9 = 0$
Question 34 :
The pair of equations 5x – 15y = 8 and $3x-9y=\frac{24}{5}$ has __________.
Question 35 :
Solve the following pair of linear equations: 21x + 47y = 110 and 47x + 21y = 162.
Question 36 :
What is/ are the algebraic method/ methods that can solve a pair of linear equations?
Question 37 :
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 38 :
A pair of linear equations is ______ if it has a unique solution.
Question 39 :
Is x = 1, y = 1 a solution of $2x + 3y = 5$?
Question 40 :
2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
Question 41 :
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 intersect at a point, are parallel or coincident: $6x – 3y + 10 = 0 ; 2x – y + 9 = 0$
Question 42 :
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 43 :
For which values of p does the pair of equations given below has unique solution?$4x + py + 8 =0 ; 2x + 2y + 2 =0$
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 :
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 46 :
A pair of linear equations is inconsistent, if it has ___________.
Question 47 :
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 48 :
A pair of linear equations which has no solution, is called an __________________ pair of linear equations.
Question 49 :
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 50 :
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 _______.
