How many solutions does this linear system have? y  = 2x  – 5       –8x  – 4y  =  –20how many?

Rearrange the first equation so it matches the second equation and then use elimination method to solve. Or substitute 2x-5 for y into the second equation and solve.  You will end up with one of the following:
--> x = some value and y = some value (ONE SOLUTION)
--> A True statement, such as 0 = 0, or 1=1, etc (INFINITELY MANY SOLN'S)
--> A False statement, such as 0 = 1, or 5 = 7, etc (NO SOLUTIONS)

Using substitution method:
-8x - 4(2x - 5) = -20
-8x - 8x + 20 = -20
     -16x         = -40
         x          = -40/16

One Solution