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# 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 - Mathematics

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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.

9x + 3y + 12 = 0, 18x + 6y + 24 = 0

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#### 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 = 9, b_1 = 3, c_1 = 12;

a_2 = 18, b_2 = 6, c_2 = 24

:.a_1/a_2=9/18=1/2,b_1/b_2=3/6=1/2

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

Thus, the lines representing the pair of linear equation coincide.

Concept: Linear Equations in Two Variables
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.2 | Q 2.2 | Page 49

#### Video TutorialsVIEW ALL [3]

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