CHAPTER-4: LINEAR EQUATIONS IN TWO VARIABLES
READ THE STATEMENTS GIVEN BELOW AND EXPRESS THEM IN EQUATION FORM:
(!) Ten years ago a man was 8 times as old as his son.
SOLUTION: Let x: man's age and y : son's age.
age of the man and his son ten years ago are : x-10 and y-10.
as the age of the man is 8 times that of his son: (x-10) = 8(y-10)
thus the equation will be : x-10 = 8(y-10)
x-10 = 8y-80
x-8y-10+80 = 0
x-8y + 70 = 0
2) Harsha and Sukirta, 2 students of class IX, together contribute Rs. 1000 to orphanage fund to help orphan children.
SOLUTION: Let x : Harsha's amount and y: Sukirta's amount, then
the equation will be as:
x + y = 1000
x + y - 1000 = 0
3) The cost of a pen is 4 times the cost of a pencil.
SOLUTION: Let x : the cost of the pen, and y : the cost of the pencil. then
the equation will be ;
x = 4y
x - 4y = 0
x - 4y + 0 = 0
4) In a quadrilateral 2 angles are equal and one of them has a measure of 53 degree.
SOLUTION: Let x : the 2 equal angles, y : unknown angle,
a quadrilateral has 4 angles. by given two angles are equal so let we take the first 2 angles as x and x.
the third angle is 53 degrees. and the fourth angle is the unknown which is y.
we know that the sum of the four angles of a quadrilateral is 360 degree.
therefore, the equation will be;
x + x+ 53 +y = 360
2x + y + 53 - 360 = 0
2x + y - 307 = 0
5) The cost of 2 sarees exceeds the cost of 3 suits by Rs. 5400.
SOLUTION: Let x : cost of the sarees, and y : cost of the suits
then the equation will be;
2x = 3y + 5400
2x - 3y - 5400 = 0
6) Vishwa bought 150 chocolates for his birthday. he distributed the chocolates in his classroom by giving 3 chocolates to each boys and 2 chocolates for each girls, he is left with 10 chocolates.
SOLUTION: Let x : boys, and y : girls
then the equation will be;
3x + 2y = 150 - 10
3x + 2y = 140
3x + 2y - 140 = 0
7) In a garden there are 5000 trees. out of this 5000 trees some are coconut trees and the others are mango trees.
SOLUTION: Let x : coconut trees, and y: mango trees.
then the equation will be;
x + y = 5000
x + y - 5000 = 0
8) The call-taxi fare in Chennai is as follows:
For the first kilometer, the fare is Rs. 50, and for the subsequent distance it is Rs. 20 per km.
SOLUTION: Let x : distance km , and y : fare Rs.
then the equation will be;
y = 50 + 20(x-1)
y = 50 + 20x - 20
y = 30 + 20x
20x - y + 30 = 0
9) The linear equation which converts temperature in degrees celsius (C) to degrees in Fahrenheit (F) is given by:
temperature in Fahrenheit is 32 more than 7/5 of the temperature in celsius.
SOLUTION: Let C: Celsius and F: Fahrenheit
F = 32 + 7/5 C
SOLUTION: Let x : the 2 equal angles, y : unknown angle,
a quadrilateral has 4 angles. by given two angles are equal so let we take the first 2 angles as x and x.
the third angle is 53 degrees. and the fourth angle is the unknown which is y.
we know that the sum of the four angles of a quadrilateral is 360 degree.
therefore, the equation will be;
x + x+ 53 +y = 360
2x + y + 53 - 360 = 0
2x + y - 307 = 0
5) The cost of 2 sarees exceeds the cost of 3 suits by Rs. 5400.
SOLUTION: Let x : cost of the sarees, and y : cost of the suits
then the equation will be;
2x = 3y + 5400
2x - 3y - 5400 = 0
6) Vishwa bought 150 chocolates for his birthday. he distributed the chocolates in his classroom by giving 3 chocolates to each boys and 2 chocolates for each girls, he is left with 10 chocolates.
SOLUTION: Let x : boys, and y : girls
then the equation will be;
3x + 2y = 150 - 10
3x + 2y = 140
3x + 2y - 140 = 0
7) In a garden there are 5000 trees. out of this 5000 trees some are coconut trees and the others are mango trees.
SOLUTION: Let x : coconut trees, and y: mango trees.
then the equation will be;
x + y = 5000
x + y - 5000 = 0
8) The call-taxi fare in Chennai is as follows:
For the first kilometer, the fare is Rs. 50, and for the subsequent distance it is Rs. 20 per km.
SOLUTION: Let x : distance km , and y : fare Rs.
then the equation will be;
y = 50 + 20(x-1)
y = 50 + 20x - 20
y = 30 + 20x
20x - y + 30 = 0
9) The linear equation which converts temperature in degrees celsius (C) to degrees in Fahrenheit (F) is given by:
temperature in Fahrenheit is 32 more than 7/5 of the temperature in celsius.
SOLUTION: Let C: Celsius and F: Fahrenheit
F = 32 + 7/5 C
