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Pair of Linear Equations in Two Variables

Short Answer Type

41.
Solve the following pairs of linear equations by the substitution method.
$space space space space space space space space fraction numerator 3 straight x over denominator 2 end fraction minus fraction numerator 5 straight y over denominator 3 end fraction equals negative 2$
$space space space space straight x over 3 plus straight y over 2 equals 13 over 6$

We have

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The given pair of linear equation is
9x - 10y = - 12 ...(i)
2x - 3y = 13 ...(ii)
From (ii), we have

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Substituting the value of x in (i), we get
9x - 10y = - 12

rightwards double arrow space 9 open parentheses fraction numerator 13 plus 3 y over denominator 2 end fraction close parentheses minus 10 y equals negative 12 rightwards double arrow space space space fraction numerator 9 left parenthesis 13 plus 3 y right parenthesis minus 20 y over denominator 2 end fraction equals negative 12 rightwards double arrow space space 11 plus 27 y minus 20 y equals negative 24 rightwards double arrow space space space minus 47 y equals negative 24 minus 117 rightwards double arrow space space space space space space space y equals 141 over 47 equals 3

Substituting the value ofy in (iii), we get

straight x equals fraction numerator 13 minus 3 straight y over denominator 2 end fraction equals fraction numerator 13 minus 3 cross times 3 over denominator 2 end fraction equals fraction numerator 13 minus 9 over denominator 2 end fraction equals 4 over 2 equals 2

Therefore, the solution is
x = 2,y = 3.
Verification. Substituting x = 2 and y = 3, we find that both the equations (i) and (ii) are satisfied as shown below :

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This verifies the solution.

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42.

Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

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43. Form the pair of linear equations for the following problems and find their solutions by substitution method.

The difference between two numbers is 26 and one number is three times the other. Find them.

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44. Form the pair of linear equations for the following problems and find their solutions by substitution method.

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

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45.

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.

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46.

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

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ` 105 and for a journey of 15 km, the charge paid is ` 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

154 Views

47.

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

A fraction becomes $9 over 11$ , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $space 5 over 6$ . Find the fraction.

171 Views

48.

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

Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

183 Views