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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. - CBSE Class 10 - Mathematics

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Question

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.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 3: Pair of Linear Equations in Two Variables
Ex. 3.20 | Q: 2.1 | Page no. 49
Solution 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. Concept: Graphical Method of Solution of a Pair of Linear Equations.
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