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

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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 = 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.

Concept: Linear Equations in Two Variables

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