How many solutions does the system of equations have? -5x+y=-18. 10x-2y=36
To determine the number of solutions in a system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution:
1) Solve the first equation for y:
-5x + y = -18
y = -5x - 18
2) Substitute this equation for y in the second equation:
10x - 2(-5x - 18) = 36
10x + 10x + 36 = 36
20x + 36 = 36
20x = 0
x = 0
3) Substitute x = 0 into any of the original equations:
-5(0) + y = -18
y = -18
Therefore, the system of equations has one solution, which is x = 0 and y = -18.