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Pair Of Linear Equations In Two Variables

Question
CBSEENMA10006529
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Form the pair of linear equations for the following problems and find their solution by substitution method.

The coach of a cricket team buys 7 bats and 6 balls for ` 3800. Later, she buys 3 bats and 5 balls for ` 1750. Find the cost of each bat and each ball.

Solution

Let the cost of each bat and each ball be Rs. x and Rs. y respectively.
According to given conditions,
7x + 6y = 3800    ...(i)
3x + 5y = 1750    ...(ii)
From eqn. (ii), we get
3x + 5y = = 1750
rightwards double arrow space space space space space 5 straight y space equals space 1750 space minus space 3 straight x rightwards double arrow space space space space space straight y space equals space 1750 space minus space 3 straight x rightwards double arrow space space space space space straight y space equals space fraction numerator 1750 space minus space 3 straight x over denominator 5 end fraction space space space space space space space space space space.... left parenthesis iii right parenthesis
Substitute the value of eqn. (iii) in (i), we get
7x + 6y = 3800
rightwards double arrow space 7 straight x space plus 6 space open parentheses fraction numerator 1750 minus 3 straight x over denominator 5 end fraction close parentheses equals 3800 rightwards double arrow fraction numerator 35 straight x plus 6 left parenthesis 1750 minus 3 straight x right parenthesis over denominator 5 end fraction equals 3800 rightwards double arrow space 35 straight x space plus space 10500 minus 18 straight x equals 19000 rightwards double arrow space 17 straight x plus 10500 equals 19000 rightwards double arrow 17 straight x space equals space 1900 minus 10500 rightwards double arrow space 17 straight x space equals space 8500 rightwards double arrow space space space space straight x space equals space 8500 over 17 equals 500
Substituting the value of x in {iii) we get,
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Hence, the cost of one bat = Rs. 500 and cost of one ball = Rs. 50.

Some More Questions From Pair of Linear Equations in Two Variables Chapter

Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

2x + y – 6 = 0,      4x – 2y – 4 = 0

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Given the linear equations 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representing of the pair so formed is :

(i) intersecting lines

(ii) parallel lines

(iii) coincident lines.

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