Pair of Linear ...

The product of two numbers is 54 and their sum is 21. Find the sum of the reciprocal of the numbers.

The sum of the digits of a two-digit number is 6. Also, twice of this number is 6 more than the number obtained by reversing the order of the digits. Find the number.

The denominator of rational number is 4 more than its numerator. The number is obtained on subtracting 1 from the numerator and adding 5 to the denominator of its reciprocal. Find the original rational number.

Find the value of k and m for which the given lines represent the pair of equations which are coincident.

9x + ky + 12 = 0
12x + 8y + m = 0

How many solutions do the following linear equations have?

7x – 8y + 6 = 0
9x + 9y – 9 = 0

If the following system of equation has no solution, which of the following can't be the values of z and k?

2x + 3y + z = 0
12x + 18y + k = 0

Arya starts his job with certain monthly salary and earns a certain increment every year. If his salary was Rs. 6,300 after 6 years of service and Rs. 7,200 after 12 years, find his initial salary and annual increment respectively.

The system of equations 1.5x + 2.5y + c = 0 and 2.25x + 3.75y + 10.8 = 0 can have many solutions, if

After adding 5 to the numerator, a new fraction is formed which is equal to ; and if 3 is subtracted from the denominator, a new fraction is formed which is equal to . Find the fraction.

A square ABCD is drawn for the following pair of lines.
3x + 6y + 15 = 0
5x + 10y + c = 0

For equations to represent the sides AB and CD, the value of 'c' can't be

If 3x + 5y + 8 = 0 and 4.2x + 8y + 11.2 = 0, then which of the following is true?

What will be the value of 34x + y, if 17x + 68y = 5, 102x + 340y = 166, and x ≠ 0 and y ≠ 0?

If the subtraction of a two digit number from the number formed by interchanging the positions of the digits of the same number gives the answer as 45, then what is the difference between the two digits of that number?

What is the value of M + N, if the following pair of equations has infinite solutions?

15x + 28y = N
22.5x + My = 19.5

The cost of 17 pencils(p) and 136 erasers(e) is Rs. 197. Which of the following equations can represent the given situation?

Jamie bought 2 bottles of lemonade and 1 packet of crisps for Rs. 140. Jennifer bought 1 bottle of lemonade and 3 packets of crisps for Rs. 170. Find the cost of a bottle of lemonade and a packet of crisps.

A cab charges a fixed amount and some additional amount for every kilometre of distance travelled. Charges for a distance of 9 km are Rs. 118 and for 16 km are Rs. 202. Find the fixed charges.

5 boys and 3 girls can finish the experiment in 6 days, while 3 boys and 6 girls can finish it in 4 days. Find the time taken by 1 boy alone to finish the whole experiment.

Ashley got 100 marks in his maths test. He got 4 marks for each right answer and lost 1 mark for each wrong answer. If 2 marks are deducted for each wrong answer instead of 1 mark, then his total score would become 80. Find the total number of questions in the test.

Sonal can row a boat to downstream 30 km in 3 hours, and to upstream 8 km in 4 hours. Find her speed of rowing in still water.

Solve for a and b in the following question.

Match the following.

Systems of Equations	Solutions
1. ,	(i) ,
2. ,	(ii) x = 20, y = 2
3. ,	(iii) ,
4. 2x - 5y = 10 3x - 6y = 12	(iv) ,

There are four pairs of equations given below. Identify the solutions for each equation as consistent or inconsistent.

(1) 2x + 10y = 32
6x – 15y = 34

(2)



(3)



(4) 0.4x + 0.3y = 2
0.8x + 0.6y = 4

Which of the following graphs represent the given pair of lines.

4 x – y = 4 and 6 x – 2 y = 6

Read the statements carefully and choose the correct option.
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both statements I and II are correct.
(d) Both statements I and II are incorrect.


Statement I: 7x - 3y = 26
(a + b )x – ( -a + b)y = 5a + b
These two equations have unique solutions, if a = 2, b = 5.

Statement II:



These two equations have infinitely many solutions.