perplexus.info :: Just Math : A meeting point

A meeting point (Posted on 2018-01-07)

The lines with equations:
y = x + 1,
y = mx − 1,
& y = −4x + 2m
pass through the same point.

Determine all possible values for m.

See The Solution Submitted by Ady TZIDON

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solution

| Comment 1 of 2

y = x+1

y = mx - 1

x+1 = mx - 1

(m-1)x = 2

x = 2/(m-1)

y = 2/(m-1) + 1

2/(m-1) + 1 = -8/(m-1) + 2m

2 + m - 1 = -8 + 2m(m-1)

2m^2 - 2m - 8 - 2 - m + 1 = 0

2m^2 - 3m - 9 = 0

m = (3 +/- sqrt(9 + 72)) / 4

m = (3 +/- sqrt(81)) / 4

m = (3 +/- 9) / 4

m = 3 or -1.5

Posted by Charlie on 2018-01-07 12:24:25

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