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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 otherThis 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»

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.



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