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Pair Of Linear Equations In Two Variables

Question
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Solve the following pairs of equations by reducing them to a pair of linear equations :

4 over straight x plus 3 straight y equals 14 3 over straight x minus 4 straight y equals 23

Solution
Let space space space space space space space 1 over straight x equals straight a

Thus, the given equations become
4a + 3y = 14    ...(i)
3a - 4y = 23    ...(ii)
For making the coefficient of ‘y’ in (i) and (ii), we multiply (i) by 4 and (ii) by 3 and then adding, we get

space space space 16 straight a plus 12 straight y equals 56 bottom enclose space space space 9 straight a minus 12 straight y space equals 69 space space space space space end enclose 25 straight a space space space space space space space space space space equals space 125 rightwards double arrow space space space space space space straight a space equals space 125 over 25 rightwards double arrow space space space space space space straight a equals 5
Putting the value of ‘a’ in (i), we get
4a + 3y = 14
rightwards double arrow space space space space space space space 4 left parenthesis 5 right parenthesis space plus space 3 straight y space equals space 14 rightwards double arrow space space space space space space space space 20 straight y space plus space 3 straight y space equals space 14 rightwards double arrow space space space space space space space space 3 straight y space equals space minus 6 rightwards double arrow space space space space space space space space space straight y space equals space minus 2 Now space space space space space space space straight a space equals space 5 rightwards double arrow space space space space space space space space space space space 1 over straight x equals 5 rightwards double arrow space space space space space space space space space space space space straight x space equals 1 fifth

Hence,  space space space space space space space space space space space space space space straight x equals 1 fifth space and space straight y space equals negative 2, is the solution of the given equation.

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.

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