In a video game, you move two androids on a coordinate grid until they totally overlap. One android is moving along the line #y=6x+5# and the other is moving along the line #y=10x-1#. At what point do the two androids meet?

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Answer 1 · 2017-01-11T23:39:32

The point of interesection is #(3/2, 14)#

A clever application of solving two linear equations!

Since each equation reads #y=# on the left, the two right sides must be equal (since both equal #y#).

#6x+5=10x-1#

We solve by collecting like terms:

#5+1=10x-6x#

#6=4x#

#x=6/4 = 3/2# This is the #x# coordinate of the point of intersection.

Now put this value of #x# into either equation to find the #y#-coordinate

#10(3/2)-1 = 15-1=14#

The point of interesection is #(3/2, 14)#