use the subsitution method to solve the system x=y-4, x+8y=2
A: infinite solutions
B: no solution
C:((2)/(3),-3(1)/(3))
D:-3(1)/(3),(2)/(3))
First, let's solve the first equation for x in terms of y:
x = y - 4
Next, substitute this expression for x into the second equation:
(y - 4) + 8y = 2
y - 4 + 8y = 2
9y - 4 = 2
9y = 6
y = 6/9
y = 2/3
Now, substitute y = 2/3 back into the first equation to find x:
x = (2/3) - 4
x = (2/3) - (12/3)
x = -10/3
x = -3 1/3
Therefore, the solution to the system is C: ((2)/(3),-3(1)/(3))