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

3 answers

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).

answer from the list

(2/3,−3 1/3)