Question

Find nature of the lines representing the linear
equations 2x - y = 3 and 4x - y = 5.
​

Answer 1

2x-y-3 = 0

4x-y-5 = 0

here, a1= 2

b1=-1

c1= -3

a2 = 4

b2 = -1

c2 = -5

so when we compare a1/a2 with b1/b2, they are unequal.

hence these two equations are intersecting i.e. have unique solutions.

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Answer 2

the nature is consistent since there is only one solution for the pair of the given linear equation.