How many soultions does this linear system have? y=2x-5 -8x-4y=-20 ?

One solution, since the lines intersect at only one point.

Step-by-step explanation:

These two equations should be separated by a comma or written on two separate lines.  I'm assuming that you meant:

y=2x-5

-8x-4y=-20

First, we need to ensure that both of these equations are written in the same format, y = mx + b.  The first equation is already in that format:  y = 2x - 5.  The  first step in rewriting the second equation is to add 8x to both sides:

+ 8x -8x -4y = 8x = -20, or -4y = 8x - 20.

Next, we divide all three terms by -4 to isolate y:

y = -2x + 5

Then the given system is equivalent to

y = 2x - 5

y = -2x + 5

We could either solve this system or analyze it without solving it:

Because these two equations have different slopes, their graphs are not parallel.  This indicates that the lines intersect at only one point.

entering that problem on the tube might get you an answer