Question

It's early in the evening, and you're standing in your back yard waiting for the stars to come out. Before long, you can see two stars in the sky. The equation of the line between you and Venus (which is actually a planet, but looks like a star) is y = 10x + 30. The equation of the line between you and Sirius is y = 9x + 40. Which star is higher in the sky? Why?

Answer 1

No star is higher; they're the same.
y = 10x + 30
Substitute "9x + 40" with y.

Then you get 9x + 40 = 10x + 30.
Get the variables on one side and the numbers on one side.
Basic algebra used here subtract 9x from both sides. Then subtract 30 from both sides and you will get x = 10.

Plug 10 for X into the equation and you will get Y = 130. Try each problem separately and you will get the same answer for both so they're equal, none is higher.