Nootan solutions for माठेमटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 5 - Simultaneous Linear Equations [Latest edition]

Solve the following simultaneous equations by the substitution method.

x + y = 3, x – 7y = –5

Solve the following simultaneous equations by the substitution method.

2x + y = 4, 3x + 2y = 7

Solve the following simultaneous equations by the substitution method.

3x + 4y = 13, 5x + 9y = 24

Solve the following simultaneous equations by the substitution method.

3x + 4y = 37, 7x + 9y = 85

Solve the following simultaneous equations by the substitution method.

3x – 2y = 0, 5x + y = 13

Solve the following simultaneous equations by the substitution method.

x + 5y = 28, 4x + 15y = 87

Solve the following simultaneous equations by the substitution method.

x + 2y = 5, 3x – y = 8

Solve the following simultaneous equations by the substitution method.

7x – 10y = 11, 3x – 7y = 2

Solve the following simultaneous equations by the substitution method.

4(x + 4) – 3(y + 2) = 5, 3(x – 1) + 2y + 1 = 24

Solve the following simultaneous equations by the substitution method.

`(2x)/3 + y/4 = 3, x/3 - y/4 = 0`

Solve the following simultaneous equations by the substitution method.

0.2x + 0.5y = 2.1, 0.3x + 0.4y = 2.8

Solve the following simultaneous equations by the substitution method.

0.4x + 0.5y = 2.5, 0.3x – 0.1y = 1.4

Solve x + y = 5 and 3x + y = 13. Hence find the value of k if 3x + ky = 16.

Solve 3x – 2y = 1 and 2x + 5y = 7. Hence find the value of k if 2x + 7y = k.

Solve the following system of equations by the elimination method:

4x + 3y = 13, x + y = 4

Solve the following system of equations by the elimination method:

5x + 8y = 44, 3x + 5y = 27

Solve the following system of equations by the elimination method:

2x – 3y = 24, x – y = 13

Solve the following system of equations by the elimination method:

2x + 5y = 9, x – y = 1

Solve the following system of equations by the elimination method:

5x + 4y = –13, x – 2y = 3

Solve the following system of equations by the elimination method:

11x – 16y = 35, 4x – 9y = 0

Solve the following system of equations by the elimination method:

`x/2 + y/3 = 3, 3x + y = 12`

Solve the following system of equations by the elimination method:

`6x - 8/y = 14, 2x - 14/y = -1`

Solve the following system of equations by the elimination method:

3x = 4 – 5y, 2x – y = 7

Solve the following system of equations by the elimination method:

x = y + 4, 4x – 9y = 11

Solve the following system of equations by the elimination method:

2(x + 1) + 3(y – 2) = 19, 3(x + 2) + 2(y – 1) = 26

Solve the following system of equations by the elimination method:

3(x – 2) + 5(y + 1) = 20, 4(x – 1) + 3(y + 3) = 22

Solve the following system of equations by the elimination method:

`(x + 1)/3 + (y - 3)/4 = 3, (x - 2)/3 + (y + 1)/2 = 5`

Solve the following system of equations by the elimination method:

18x + 23y = –5, 23x + 18y = 5

Solve the following system of equations by the elimination method:

0.7x + 0.3y = 1.1, 0.2x + 0.5y = –0.1

Solve the following system of equations by the elimination method:

`x/a + y/b = a + b, x/a^2 + y/b^2 = 2, a ≠ 0, b ≠ 0`

Solve the following system of equations by the elimination method:

`x/a = y/b; ax + by = a^2 + b^2, a ≠ 0, b ≠ 0`

Solve the following system of equations by the elimination method:

(a – b)x + (a + b)y = a² – 2ab – b², (a + b) (x + y) = a² + b²

Solve the following system of equations by the elimination method:

2bx + ay = 2ab, bx – ay = 4ab

Solve the following system of equations by the elimination method:

x + y = a – b, ax – by = a² + b²

Can the following system of equations hold simultaneously?

5x + 2y = 26

2x + 3y = 17

3x + 5y = 27

If the system of the following equations hold simultaneously, find the value of k.

4x + 3y = 11

x – y = 1

3x + ky = 10

Using cross-multiplication method, solve the following system of simultaneous linear equations:

3x + 2y = 7, 2x + 3y = 8

Using cross-multiplication method, solve the following system of simultaneous linear equations:

3x + 4y = 25, 4x + 5y = 32

Using cross-multiplication method, solve the following system of simultaneous linear equations:

4x + 3y = 5, 2x + 5y = –1

Using cross-multiplication method, solve the following system of simultaneous linear equations:

2x – y = 9, 5x + y = 26

Using cross-multiplication method, solve the following system of simultaneous linear equations:

3x – 7y = 2, 4x – 3y = 9

Using cross-multiplication method, solve the following system of simultaneous linear equations:

x – 3у – 5 = 0, 3x + 2y – 8 = 0

Using cross-multiplication method, solve the following system of simultaneous linear equations:

x – 2y + 1 = 0, x + y + 4 = 0

Using cross-multiplication method, solve the following system of simultaneous linear equations:

9x – 4y = 200, 7x – 3y = 200

Solve the following system of equations by the method of cross-multiplication:

ax + by = a – b

bx – ay = a + b

Using cross-multiplication method, solve the following system of simultaneous linear equations:

5x + 7y = 31, 7x + 5y = 29

Solve the following pair of linear equations:

`9/x + 2/y = 4, 12/x + 6/y = 7, x ≠ 0, y ≠ 0`

Solve the following pair of linear equations:

`8/x + 1/y = 3, 16/x - 3/y = 1, x ≠ 0, y ≠ 0`

Solve the following pair of linear equations:

`2/x + 2/y = 1, 6/x - 9/y = -2, x ≠ 0, y ≠ 0`

Solve the following pair of linear equations:

`1/(2x) - 3/(4y) = 1, 4/x - 1/y = 3, x ≠ 0, y ≠ 0`

Solve the following pair of linear equations:

3x + 5y = 2xy, 21x – 15y = 4xy, x ≠ 0, y ≠ 0

Solve the following pair of linear equations:

7x + 4y = 6xy, x + 3y = – 4xy, x ≠ 0, y ≠ 0

Solve the following pair of linear equations:

`7x - 4y = 3/2 xy, x + y = 7/2 xy, x ≠ 0, y ≠ 0`

Solve the following pair of linear equations:

`9/sqrt(x) + 2/sqrt(y) = 4, 3/sqrt(x) + 4/sqrt(y) = 3, x ≠ 0, y ≠ 0`

Solve the following pair of linear equations:

`10/(x + 1) - 2/(y - 1) = 3/2, 5/(x + 1) + 8/(y - 1) = 3`

Solve the following pair of linear equations:

`4/(x + 2) - 6/(y - 1) = -1, 2/(x + 2) + 3/(y - 1) = 1`

Solve the following pair of linear equations:

`10/(x + y) - 1/(x - y) = 1, 5/(x + y) + 3/(x - y) = 4`

Solve the following pair of linear equations:

`6/(2x + y) + 5/(2x - y) = 3, 9/(2x + y) - 10/(2x - y) = 1`

The sum of two numbers is 40 and their difference is 16. Find the numbers.

The sum of two numbers is 28. Thrice the smaller is 20 more than the larger. Find two numbers.

The sum of two numbers is 35. If twice the smaller added to larger, the result is 50. Find the numbers.

Two numbers are in the ratio 8 : 9. If 12 is added to both the numbers, their ratio becomes 12 : 13. Find the numbers.

If one is added to both numerator and denominator of a fraction, it becomes `1/2`. If 2 is added to the denominator of the fraction, it becomes `1/3`. Find the fraction.

The sum of numerator and denominator of a fraction is 18. If 3 is added to both numerator and denominator of the fraction it becomes `1/2`. Find the fraction.

The unit digit of a two digit number is 1 more than twice its tens digit. If the digits are reversed, the new number is 45 more than the original number. Find the number.

The tens digits of a two digit number is one more than thrice the unit digit. The sum of its digits is 9. Find the number.

The sum of digits of a two digit number is 8. If 18 is added to the number, its digits interchange. Find the number.

The ratio of the annual income of A and B is 5 : 4 and the ratio of their expenditures is 11 : 8. If each saves ₹ 4000. Find their annual incomes.

The ratio of the annual income of A and B is 6 : 5 and the ratio of their expenditures is 5 : 4. If each saves ₹ 10000, find their annual incomes.

A is 12 years older than B. 4 years ago, A was twice as old as B. Find the present ages of A and B.

6 years hence, Ravi will be twice as old as his son. 18 years ago, Ravi was six times of his son’s age. Find their present ages.

The present age of Sharman is twice the sum of the ages of his two sons. Six years ago, his age was 5 times the sum of the ages of two sons. Find the present age of Sharman.

The cost of 3 notebooks and 5 pens is ₹ 265. The cost of 2 notebooks and 9 pens is ₹ 205. Find the cost of one notebook and cost of one pen.

The railway fare from Delhi to Meerut for 3 adults and 2 children is ₹ 250 and for 2 adults and 3 children is ₹ 225. Find the fare for one adult and for one child.

A person divides some money among some students equally. If there were 5 more students, each student will get ₹ 4 less. If there were 5 students less, each student will get ₹ 6 more. Find the total money.

A and B have some money with them. B said to A if you give me ₹ 50, my money will be equal to your money. A said to B if you give me ₹ 100, my money will be equal to four times of your money. How much money did A and B have initially?

Shama has some ₹ 2 and some ₹ 5 coins. The total number of coins are 50 and their total cost is ₹ 190. Find the number of ₹ 2 coins and of ₹ 5 coins.

Two places A and B are 120 km apart on a highway. A car starts from A and another starts from B at the same time. If they go in the same direction they meet in 3 hours. If they go in opposite direction, they meet in one hour. Find the speeds of car A and car B.

A shopkeeper purchases a table and a chair for ₹ 1400. If he sold them for ₹ 1630, he makes a profit of 20% on the table and 10% on the chair. Find the cost of one table and that of one chair.

2 men and 5 boys together can do a piece of work in 4 days while 1 man and 2 boys together can do the same work 9 days. Find the time taken by : (a) one man alone, (b) one boy alone to complete the work.

The result of dividing two digit number by the number with digits reversed is `1 3/4` and the sum of the digits of number is 9. Find the number.

The fare of a taxi is fixed and the remaining depends on the distance covered per km. Rahim goes 30 km by a taxi and paid ₹ 400 while Kamal goes 40 km by a taxi and paid ₹ 500. Find the fixed fare and the fare per km.

Half the perimeter of a rectangular garden whose breadth is 4 m less than its length of 36 m. Find the length and breadth of the garden.

The area of a rectangle gets reduced by 9 sq. 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 breadth by 2 units, then the area is increased by 67 sq. units. Find the length and breadth of the rectangle.

The students of a class are made to stand in rows (complete). If one student is extra in a row, there would be 2 rows less and if one student is less in a row, there would be 3 rows more. Find the number of students in the class.

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.

A boat goes 44 km downstream in 4 hours and takes 4 hours 48 minutes longer in the same return journey. Find the speed of boat in still water and the speed of current.

Kavita travels 28 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 4 km by rickshaw and the remaining distance by bus. If she travels 8 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed to rickshaw and the speed of the bus.

In a ΔАВС, ∠C = 3 ∠B = 2(∠A + ∠B). Find all angles of ΔАВС.

Ravi invests some money at 12% simple interest and some other money at 10% simple interest and receives ₹ 2600 as yearly interest. If he had interchanged the amounts, he would have received ₹ 80 more as yearly interest. How much did he invest at different rates?

If x + 2y = 7 and 3x + y = 6, then (x, y) is equal to ______.

If 2x + 3y = –5 and 3x + 2y = 0, then x is equal to ______.

If 34x + 43y = –9, 43x + 34y = 9, then x + y is equal to ______.

If x + y = 5 and x – y = 3 then 3x + 2y is equal to ______.

If x = 2 – y and 2y = x – 11 then the value of y is ______.

If `2/x + 3/y = 13` and `5/x - 4/y = -2` then (x, y) is equal to ______.

If `20/(x + y) + 3/(x - y) = 7` and `8/(x - y) - 15/(x + y) = 5` then (x, y) is ______.

x = a, y = b is the solution of the pair of equations 3x + y = 10 and x – y = 2, then (a, b) is equal to ______.

If `2x - 3/y = 9` and `3x + 7/y = 2` then the value of x is ______.

(a – b)x + (a + b)y = a² – 2ab – b², (a + b)(x + y) = a² + b² gives the following solution:

(i) The sum of two numbers is 40 and their difference is 8. The numbers will be 24 and 16.

(ii) If x + 3y = 10 and x + y = 4 then x = 2.

(i) lf 77x + 63y = 123 and 63x + 77y = 17 then x + y = 5.

(ii) 3x + 2y = 7 and 2x + 3y = 8 gives x = 2, y = 1.

(i) The solution of 3x + 4y = 25 and 4x + 5y = 32 is x = 2, y = 1.

(ii) x = 1, y = 1 is a solution of ax + by = a + b.

(i) x = 3, y = 1 is a solution of 9x – 7y = 20.

(ii) x = 4, y = –1 is a solution of x – y = 5.