# On Comparing the Ratios a 1 a 2 , B 1 B 2 and C 1 C 2 Without Drawing Them, Find Out Whether the Lines Representing the Following Pair of Linear Equations Intersect at a Point, Are - Mathematics

Sum

On comparing the ratios a_1/a_2,b_1/b_2 and c_1/c_2 without drawing them, find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincide.

6x – 3y + 10 = 0, 2x – y + 9 = 0

#### Solution

Comparing the given equations with standard forms of equations a_1 x + b_1 y + c_1 = 0 and a_2 x + b_2 y + c_2 = 0

we have
a1 = 6, b_1 = – 3, c_1 = 10;

a_2 = 2, b_2 = – 6, c_2 = 9

:.a_1/a_2=6/2=3, b_1/b_2=(-3)/-1=3

=>a_1/a_2=b_1/b_2!=c_1/c_2

Thus, the lines representing the pair of linear equations are parallel.

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#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.2 | Q 2.3 | Page 49