Question

SPOTLIGHTS Ship A has coordinates (–1, –2) and

Answer 1

Answer:

The lifeboat has coordinates (5,10).

Step-by-step explanation:

The equation $y=2x$ represents the light beam from Ship A, which has coordinates $(-1,-2)$.

The equation $y=x+5$ represents the light beam from Ship B, which has coordinates $(-4,1)$.

This problem models a system of linear equations, because we need to find the coordinates of the lifeboat, which is a common points for both ships. So, basically, we just need to find the solution for the system formed by both equations.

$y=2x\\y=x+5$

We multiply the first equation by -1, and then sum

$-y=-2x\\y=x+5$

$0=-x+5\\-5=-x\\x=5$

Now, we use this value to find the other one

$y=2x=2(5)=10$

Therefore, the lifeboat has coordinates (5,10).

The image attached shows the solution graphically.