Use the substitution method to solve the system x=y−4 , x+8y=2 .
(2/3,−3 1/3)
(−3 1/3,2/3)
infinite solutions
no solution
Let's solve the given system of equations using the substitution method.
From the first equation, we can express x in terms of y as x = y - 4.
Now substitute this value of x in the second equation:
(y - 4) + 8y = 2
Combine like terms:
9y - 4 = 2
Add 4 to both sides:
9y = 6
Divide both sides by 9:
y = 2/3
Now substitute the value of y in the first equation:
x = (2/3) - 4
Simplify:
x = -11/3
Therefore, the solution to the system of equations is (x,y) = (-11/3, 2/3).
So, the correct answer is (-11/3, 2/3).