How many solutions does the system of equations have?
-5x+y=-18
10x-2y=36
To find the number of solutions for this system of equations, we can use the method of elimination or substitution.
Let's solve using the method of elimination:
Multiply the first equation by 2 to eliminate the y terms:
-10x + 2y = -36
Now, add the two equations together:
(10x - 2y) + (-10x + 2y) = 36 + (-36)
0 = 0
The result is 0 = 0. This equation is always true, indicating that the two original equations are dependent. This means that they represent the same line and there are infinitely many solutions.