Question

The lines 2x+5y=17 and 5x+3y=14 are consistent.

(a) False

(b) True

I got this question in an interview.

The question is from Solution of Two Linear Equations in Two Variables in Different Methods topic in portion Pair of Linear Equations in Two Variables of Mathematics – Class 10

Answer 1

The correct answer is (b) True

Best explanation: A system of linear equations is said to be consistent if it has at least one solution.

The given equations are 2x+5y=17 and 5x+3y=14

Here, a1=2, b1=5, c1=-17 and a2=5, b2=3, c2=-14

Now, \(\frac {a_1}{a_2} =\frac {2}{5}, \frac {b_1}{b_2} =\frac {5}{3}, \frac {c_1}{c_2} =\frac {-17}{-14}\)

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

Hence, it will have unique solution.

The given equations are consistent.