Question

How many solutions exist for the system y = 2x + 5 and y = -0.2x - 4?
no solution
one solution
infinitely many solutions

Answer 1

Here's a quick way to figure this out:

Step 1) Identify the slopes of each line


Step 2) If the slopes are equal then jump to step 2a). If the slopes are NOT equal, then you'll have exactly one solution.

Step 2a) ***Do this step only if the slopes are equal***. If the y-intercepts are NOT equal, then there are no solutions. If the y-intercepts are equal, then you have an infinite number of solutions