Form the pair of linear equations in the following problems, and

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 Multiple Choice QuestionsShort Answer Type

111.

For what values of a and b does the following pair of linear equations have an enfinitc no. of solution :

2x + 3y = 7
a (x + y) -b (x - y) = 3a + b - 2

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112.

Solve the following pair of linear equations by the elimination method and the substitution method
x + y = 5 and 2x – 3y = 4

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113.

Solve the following pair of linear equations by the elimination method and the substitution method
3x + 4y = 10 and 2x – 2y = 2

215 Views

114.

Solve the following pair of linear equations by the elimination method and the substitution method
3x – 5y – 4 = 0 and 9x = 2y + 7

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115.

Solve the following pair of linear equations by the elimination method and the substitution method

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116.

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to It becomes   1 half if we only add I to the denominator. What is the fraction?


Let the numerator of the fraction x and denominator be y. Then


space space space Fraction space equals space straight x over straight y
Then, according to given conditions,

Case space straight I. space space space space space space space fraction numerator straight x plus 1 over denominator straight y minus 1 end fraction equals 1
rightwards double arrow space space space space space space space straight x plus 1 equals straight y minus 1
rightwards double arrow space space space space space space space straight x minus straight y equals negative 2
space


Case space II. space fraction numerator straight x over denominator straight y plus 1 end fraction equals 1 half
rightwards double arrow space space 2 straight x space equals space straight y plus 1
rightwards double arrow space 2 straight x minus straight y equals 1

Thus, we have following equation
x - y = -2    ...(i)
2x - y = 1    ...(ii)
From (i), we have
x - y = -2
⇒    x = y - 2    ...(iii)
Substituting the value of x in (ii), we get
2x - y = 1
⇒ 2(y - 2) - y = 1
⇒ 2y - 4 - y = 1
⇒    y - 4 = 1⇒    >> y = 5
Now, substituting the value ofy in (iii), we get
x = y - 2
= 5 - 2 = 3
Hence, the required fraction equals 3 over 5

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117.

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

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118.

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

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119.

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

Meena went to a bank to withdraw ` 2000. She asked the cashier to give her ` 50 and ` 100 notes only. Meena got 25 notes in all. Find how many notes of ` 50 and ` 100 she received.

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120.

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ` 27 for a book kept for seven days, while Susy paid ` 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day. 

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