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Pair Of Linear Equations In Two Variables

Question

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For what value of m, the pair of linear equations mx = 2y, 2x - y + 5 = 0 has unique solution.

Solution

Given pair of linear equations are :

mx space equals space 2 straight y rightwards double arrow space mx space minus space 2 straight y space equals space 0 and space 2 straight x minus straight y plus 5 space equals space 0

Here, we have

straight a subscript 1 equals straight m subscript 1 comma space space straight b subscript 1 equals negative 2 and space straight a subscript 2 equals 2 comma space straight b subscript 2 equals negative 1

For unique solution :

straight a subscript 1 over straight a subscript 2 not equal to straight b subscript 1 over straight b subscript 2 rightwards double arrow space space straight m over 2 not equal to fraction numerator negative 2 over denominator negative 1 end fraction rightwards double arrow space straight m not equal to 4

∴ The given system of equations has unique solution for all real values of k other than 4.

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

(i) 10 students of Class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.

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