Question

What will be the nature of the graph lines of the equations 2x+5y+15 and 6x+15y+45?

(a) Parallel

(b) Coincident

(c) Intersecting

(d) Perpendicular to each other

I got this question in an interview for job.

This intriguing question comes from Solution of Two Linear Equations in Two Variables in Different Methods in division Pair of Linear Equations in Two Variables of Mathematics – Class 10

Answer 1

The correct answer is (b) Coincident

Explanation: The given equations are 2x+5y+15 and 6x+15y+45.

Here, a1=2, b1=5, c1=15 and a2=6, b2=15, c2=45

Now, \(\frac {a_1}{a_2} = \frac {2}{6} = \frac {1}{3}, \frac {b_1}{b_2} = \frac {5}{15} =\frac {1}{3}, \frac {c_1}{c_2} = \frac {15}{45} = \frac {1}{3} \)

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

Therefore, the graph lines of the equations will be coincident.