How many solutions exist for the system y = 2x + 5 and y = -0.2x - 4?

Question

anonymous · Answer

Equate both the equations first..
let us see what you will get...

anonymous · Answer

i.e. solve 
$$ 2x + 5 =-0.2x - 4$$ for $x$

anonymous · Answer

2.2x = -9

x = -9/2.2 = 4.1(approx)

So, y = 13.2 is the only 1 value of y..

phi · Answer

You could answer the question by thinking like this
 y = 2x + 5 is the equation of a line with +2 as its slope.  It goes up and to the right
y = -0.2x - 4 is the equation of a line with slope -0.2.  It goes down and to the right

Because the lines are infinitely long and they go in different directions they must cross somewhere.  And they are straight lines (don't loop around), so they meet only once.  
So there is exactly one solution.