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i.e.

and and

3k - 3 = 2k - 1
and 2k + 1 k - 1
and 6k + 3 2k - 1
k = 2
and k - 2
and k - 1
Hence, the given system of linear equations has no solution, when k = 2

Example 5: In the following system of equations determine whether it has unique, no
or infinitely many solutions.
and
Solution: Here, given system of equations is
2x + 3y = 7
6x + 5y = 11
a 1 = 2, b 1 = 3, c 1 = 7
a 2 = 6, b 2 = 5, c 2 = 11

Therefore, it has unique solution.

Example 6: Points A and B are 70 km apart on a highway. A car starts from A and
another car starts from B simultaneously. If they travel in the same direction at different
speeds, they meet in 7 hours but if they travel towards each other, they meet in one
hour. Find the speeds of the two cars.
Solution:

Let the speed of the car which starts from the point A be x km/hr and speed of the car
which starts from the point B be y km/hr.

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