# 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?

Jan 11, 2017

The point of interesection is $\left(\frac{3}{2} , 14\right)$

#### Explanation:

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 $y$).

$6 x + 5 = 10 x - 1$

We solve by collecting like terms:

$5 + 1 = 10 x - 6 x$

$6 = 4 x$

$x = \frac{6}{4} = \frac{3}{2}$ This is the $x$ coordinate of the point of intersection.

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

$10 \left(\frac{3}{2}\right) - 1 = 15 - 1 = 14$

The point of interesection is $\left(\frac{3}{2} , 14\right)$