How many solution(s) does the system of equations have?
−5x+y=−18
10x−2y=36
To determine the number of solutions for the system of equations, we can use the method of substitution:
First, solve the first equation for y:
-5x + y = -18
y = -18 + 5x
Next, substitute this value of y into the second equation:
10x - 2(-18 + 5x) = 36
10x + 36 - 10x = 36
36 = 36
The given equation 36 = 36 is true, which means that the two equations represent the same line. In other words, these two equations are dependent, and there are infinitely many solutions.