# ICSE Worksheet for chapter-13 Linear Equations in Two Variables class 9

## Find ICSE Worksheet for chapter-13 Linear Equations in Two Variables class 9

CLASS-9

BOARD: ICSE

Mathematic Worksheet - 13

TOPIC: Linear Equations in Two Variables

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#### SUMMARY:

Standard form of linear equations:

Standard form refers to all positive coefficients.

a1x+b1y+c1z = 0 ...(i)

a2x+b2y+c2z = 0 ...(ii)

For solving such equations, we have three different methods.

1. Elimination by substitution
2. Elimination by equating the coefficients
3. Elimination by cross multiplication

#### EXERCISE:

1. A two digit number is such that product of its digits is 18. When 63 is subtracted from the number, the digits interchange their place. Find the number.
2. The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, find the numbers.
3. Rs. 9000 was divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Then find the original no. of persons.
4. A and B each has a certain number of mangoes. A says to B, ‘If you give 30 of your mangoes I will have twice as many as left with you.’ Find how many mangoes did each have.
5. For what value of k, the system of linear equations 2x+ky =1; 3x-5y=7 has a unique solution:
1. K ≠ - 10/3
2. K ≠ 10/3
3. K ≠ -35
4. K = - 10/3
6. Solve for x and y : 7/3x -6/2y =15; 8/ 3x =9/2y.
1. -3, -2
2. -2, -3
3. - 1/2, - 1/3
4. - 1/3, -1/2
7. Sum of two numbers is 35; their difference is 13.Find the numbers
1. 23, 12
2. 24, 11
3. 23, 10
4. 22, 9
8. The digit in the ten’s place of a two digit no. is three times that in the one’s place. If the digits are reversed, the new number will be 36 less than the original number. Find the number.
1. 64
2. 52
3. 62
4. 42
9. Denominator of a rational number is 4 less than its numerator. If 11 is added to the numerator and 1 is subtracted from denominator the new number becomes . Find the rational number.
1. 23/27
2. 27/23
3. 13/17
4. 17/13
10. The sum of the present ages of father and his son is 60 years. 6 years ago, father’s age was five times the age of his son. After six years son’s age will be:
1. 20 years
2. 14years
3. 12 years
4. 18 years

### Solutions: to worksheet-13 Topic-Linear Equations in Two Variables

1. 92
2. x = 1411, y = 1079
3. 25
4. A = 34, B = 62
5. (a)
6. (b)
7. (b)
8. (c)
9. (d)
10. (a)