Question

What will be the nature of the graph lines of the equations x+3y-2 and 2x-y+5?

(a) Parallel

(b) Coincident

(c) Intersecting

(d) Perpendicular to each other

This question was addressed to me by my college professor while I was bunking the class.

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

Answer 1

Correct answer is (c) Intersecting

Easy explanation: The given equations are x+3y-2 and 2x-y+5.

Here, a1=1, b1=3, c1=-2 and a2=2, b2=-1, c2=5

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

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

Therefore, the graph lines of the equations will intersect at a point.