graph solutions

[Jamie27]

Which of the following describes the graph of the solutions to the system

{ 2x+5y=-27
10y=-4x ?

I was thinking it was D because the others dont seem to fit right?

A) two intersecting lines,solution of (5,1)
B) two intersecting lines,solution of (-1,5)
C) one line, infinately many solutions
D) two parallel lines, no solutions

Thank you!

 

[galactus]

You're correct. Do you see why, besides that the others don't fit right?.

Solve each equation for y and set equal to one another, solve for x.

Let's see what happens:

\(\displaystyle \frac{-27-2x}{5}=\frac{-2x}{5}\)

\(\displaystyle =>\frac{-27-2x}{5}+\frac{2x}{5}=0\)

\(\displaystyle =>\frac{-27-2x+2x}{5}=0\)

\(\displaystyle =>\frac{-27}{5}=0\)

Oops. An obvious contradiction, so there is no solution, thus, the lines are parallel. Besides that, the slopes are the same, \(\displaystyle \frac{-2}{5}\). Which indicates they are parallel.
See?.