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Pair Of Linear Equations In Two Variables

Question
CBSEENMA10006928
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Nitish went to winter sale at Kamla Nagar to purchase some shirts and jackcts. When his friend asked him how many of each he had bought, he answered. “The number of jackets is three less than four times the number of shirts purchased. Also the number of jackets is four less than five times the numbers of shirts purchased.” Help his friends to find how many shirts and jackets Nitish bought. Express the solution graphically.

Solution

Let the number of shirts be x and the number of jackets be y. Then equations formed are
y = 4x - 3    ...(i)
y = 5x - 4    ...(ii)
We have    y = 4x - 3
Thus, we have following table :

We have    y = 5x - 4
Thus, we have following table :

Fig. 3.23.

When we plot the graph of both the equations, we find that the two lines intersect at the point (1, 1). So,x = 1,y - 1 is the required solution of the pair of linear equation i.e., the number of jackets he purchased is 1 and the number ofshirts he purchased is 1.

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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