Question

The lines 5x-7y=13 and 10x-14y=15 are inconsistent.

(a) True

(b) False

The question was posed to me during an interview.

I'd like to ask this question from Solution of Two Linear Equations in Two Variables in Different Methods in portion Pair of Linear Equations in Two Variables of Mathematics – Class 10

Answer 1

Correct choice is (a) True

For explanation I would say: A system of linear equations is said to be inconsistent if it has no solution at all.

The given equations are 5x-7y=13 and 10x-14y=15

Here, a1=5, b1=-7, c1=-13 and a2=10, b2=-14, c2=-15

Now, \(\frac {a_1}{a_2} = \frac {5}{10}=\frac {1}{2}, \frac {b_1}{b_2} =\frac {-7}{-14}=\frac {1}{2}, \frac {c_1}{c_2} =\frac {-13}{-15}\)

Clearly, \(\frac {a_1}{a_2} =\frac {b_1}{b_2} \ne \frac {c_1}{c_2}\)

Hence, it will have no solution.

The given equations are inconsistent.