How many solution(s) does the system of equations have? -5x+y=-18 and 10x-2y=36

Answer 1

To find the number of solutions, we can solve the system of equations.

Let's multiply the first equation by 2 to make the coefficients of y in both equations equal:

-5x + y = -18
2*(-5x + y) = 2*(-18)
-10x + 2y = -36

Now we have:

-10x + 2y = -36
10x - 2y = 36

Adding these two equations, we eliminate the variable x:

(-10x + 2y) + (10x - 2y) = -36 + 36
0 = 0

The equation 0 = 0 is always true, which means that the two equations are dependent. This implies that the equations represent the same line, and therefore, the system of equations has infinitely many solutions.