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Pair Of Linear Equations In Two Variables

Question
CBSEENMA10006739
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Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Solution

Let the speed of the car starting from point A be .v km/h and speed of the car starting from point B be y km/hr.

Case I. When they travel in the same direction, let they meet at point P (Fig. 3.12).
So, AP = distance covered by first car from point A to P
= speed x time
= x × 5 = 5
and    BP = distance covered by second car from point B to P
= speed × time
= y × 5 = 5y
Therefore, AB = AP - BP
⇒ 100 = 5x - 5y
⇒ 5a - 5y = 100
⇒ x - y = 20
Case II. (Fig. 3.13)
When they travel in opposite direction, let they meet at point Q.
So, AQ = Distance covered by first car from point A to Q
= Speed × Tinte
= x × 1 = x
and    BQ = Distance covered by second car from point B to Q
= Speed × Time
= y × 1 = y
Therefore, AB = AQ + BQ
⇒    100 = x + y
⇒ x + y = 100
Thus, we have following eqn.
x - y = 20
x + y = 100
⇒ x - y - 20 = 0
x + y - 100 = 0

Hence, speed of the car that starts from point A = 60 km/hr
Speed of the car that starts from point B = 40 km/hr.

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.

Given the linear equations 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representing of the pair so formed is :

(i) intersecting lines

(ii) parallel lines

(iii) coincident lines.

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