Use the substitution method to solve the system x=y−4 , x+8y=2 .(1 point)
Responses
no solution
(−3 1/3,2/3)
(2/3,−3 1/3)
infinite solutions
To solve the system of equations using the substitution method, we'll start by solving the first equation for x:
x = y - 4
We can now substitute this expression for x in the second equation:
(y - 4) + 8y = 2
Simplifying this equation gives us:
9y - 4 = 2
Adding 4 to both sides, we get:
9y = 6
Dividing both sides by 9, we find:
y = 6/9
Simplifying the fraction, we have:
y = 2/3
Now that we know the value of y, we can substitute it back into the first equation to find the corresponding value of x:
x = (2/3) - 4
Simplifying, we get:
x = -10/3
Therefore, the solution to the system of equations using the substitution method is:
(x, y) = (-10/3, 2/3)
So the correct answer is (-10/3, 2/3).