To determine the number of solutions, we can solve the system of equations using any method (substitution, elimination, etc.).
Let's solve the system using the elimination method:
-5x + y = -18 (equation 1)
10x - 2y = 36 (equation 2)
We can multiply equation 1 by 2 to obtain:
-10x + 2y = -36 (equation 3)
Adding equation 2 and equation 3, we get:
(10x - 2y) + (-10x + 2y) = 36 + (-36)
0 = 0
This equation tells us that 0 = 0, which is always true. This means that the two equations are equivalent and represent the same line.
Since the equations represent the same line, they have infinitely many solutions.
Therefore, the correct answer is:
b) infinite
how many solutions does the sytems of eqations have
-5x+y= -18 10x-2y=36
a two
b infinite
c none
d one
1 answer