Question

What will be the nature of the graph lines of the equations 5x-2y+9 and 15x-6y+1?

(a) Parallel

(b) Coincident

(c) Intersecting

(d) Perpendicular to each other

I had been asked this question in unit test.

The above asked question is from Solution of Two Linear Equations in Two Variables in Different Methods in chapter Pair of Linear Equations in Two Variables of Mathematics – Class 10

Answer 1

Right choice is (a) Parallel

To explain: The given equations are 5x-2y+9 and 15x-6y+1.

Here, a1=5, b1=-2, c1=9 and a2=15, b2=-6, c2=1

Now, \(\frac {a_1}{a_2} = \frac {5}{15} = \frac {1}{3}, \frac {b_1}{b_2} = \frac {-2

}{-6}=\frac {1}{3}, \frac {c_1}{c_2} = \frac {9}{1} \)

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

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