Intersection Of Two Lines Condition

Geometry Level 2

Let a , b , c a, b, c , and d d be constants such that ( a , b ) ≠ ( c , d ) (a,b) \neq (c,d) . Under which condition does the equation a x + b = c x + d a x+ b = c x + d have exactly one solution?

a = c a = c b ≠ d b \ne d a ≠ c a \ne c b = d b= d

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Mohamed Aly by Mohamed Aly , 49, Egypt

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2 solutions

ax+b=cx+d, then x=(d-b) \ (a-c) has one solution, then a-c cannot be zero(fraction denominator) so a different from c.

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Mohamed Aly
Mar 11, 2016

If the slopes of the two sides are not equal then the two straight lines will have a unique intersection

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3x +5 = 2x + 5. I believe the solution is zero.

Julian Fuller - 5 years, 3 months ago

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But the question asked for non-zero solution?

Ne-ko Nya - 5 years, 3 months ago

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