Answer: Infinitely many solutions
Step-by-step explanation:
Each left hand side is equal to the same thing on the right (2x)
We can equate the left hand sides to solve for y.
5(-2+3y) = 15y-10
-10+15y = 15y-10
15y-10 = 15y-10
We get the same thing on both sides. This will lead to infinitely many solutions. The infinitely many solutions are all on the line 2x-15y = -10.
All solution points are of the form (x,y) = (7.5k-5,k) where k is any real number.
For instance,
- If k = 0 then we get (x,y) = (-5,0)
- If k = 2, then we get (x,y) = (10,2)
- If k = 4, then we get (x,y) = (25,4)
- If k = 8, then we get (x,y) = (55,8)
- And so on.
Because this system has infinitely many solutions, we consider it consistent and dependent. You can use a graphing app like Desmos or GeoGebra to confirm the answer is correct.