On comparing the ratios a1/a2,b1/b2 and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide. - 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.

5x – 4y + 8 = 0, 7x + 6y – 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 = 5, b_1 = – 4, c_1 = 8;

a_2 = 7, b_2 = 6, c_2 = – 9

:.a_1/a_2=5/7,b_1/b_2=(-4)/6

=>a_1/a_2!=b_1/b_2

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

Concept: Graphical Method of Solution of a Pair of Linear Equations
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.1 | Q 5 | Page 12
NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.2 | Q 2.1 | Page 49