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# Obtain the Condition for the Following System of Linear Equations to Have a Unique Solution Ax + By = C Lx + My = N - CBSE Class 10 - Mathematics

ConceptPair of Linear Equations in Two Variables

#### Question

Obtain the condition for the following system of linear equations to have a unique solution

ax + by = c

lx + my = n

#### Solution

The given system of equations may be written as

ax + by - c = 0

lx + my - n = 0

It is of the form

a_1x + b_1y + c_1 = 0

a_2x + b_2y + c_2 = 0

Where a_1 = 1, b_1 = 2, c_1 = -c

And a_2 = l, b_2 = m,c_2 = -n

For unique solution, we must have

a_1/a_2 != b_1/b_2

=> a/l != b/m

=> am != bl

Hence, am != bl is the required condition.

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Solution Obtain the Condition for the Following System of Linear Equations to Have a Unique Solution Ax + By = C Lx + My = N Concept: Pair of Linear Equations in Two Variables.
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