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Pair of Linear Equations in Two Variables

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Question

For a pair of linear equations a1x+b1y+c1=0a_1x+b_1y+c_1=0 and a2x+b2y+c2=0a_2x+b_2y+c_2=0, what is the condition for the lines to be intersecting?

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Answer

The lines are intersecting and have a unique solution if the ratio of coefficients satisfies: a1a2≠b1b2\frac{a_1}{a_2} \neq \frac{b_1}{b_2} This is a consistent pair of equations.

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