SPOTLIGHTS Ship A has coordinates (–1, –2) and
Ship B has coordinates (–4, 1). Both ships have their
spotlights fixated on the same lifeboat. The light beam
from Ship A travels along the line y = 2x. The light
beam from Ship B travels along the line y = x + 5.
What are the coordinates of the lifeboat?

Question

04-05-2020
Mathematics

contestada

SPOTLIGHTS Ship A has coordinates (–1, –2) and
Ship B has coordinates (–4, 1). Both ships have their
spotlights fixated on the same lifeboat. The light beam
from Ship A travels along the line y = 2x. The light
beam from Ship B travels along the line y = x + 5.
What are the coordinates of the lifeboat?

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Anyone have the answer???????????

jajumonac jajumonac · Answer 1 · 2020-05-10T02:32:29+02:00

Answer:

The lifeboat has coordinates (5,10).

Step-by-step explanation:

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

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

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.

[tex]y=2x\\y=x+5[/tex]

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

[tex]-y=-2x\\y=x+5[/tex]

[tex]0=-x+5\\-5=-x\\x=5[/tex]

Now, we use this value to find the other one

[tex]y=2x=2(5)=10[/tex]

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

The image attached shows the solution graphically.