Use the substitution method to solve the system x=y−4, x+8y=2.(1 point)

Responses

(−313,23)
left parenthesis negative 3 Start Fraction 1 over 3 End Fraction comma Start Fraction 2 over 3 End Fraction right parenthesis

no solution
no solution

(23,−313)
left parenthesis Start Fraction 2 over 3 End Fraction comma negative 3 Start Fraction 1 over 3 End Fraction right parenthesis

infinite solutions

3 answers

To solve the system using the substitution method, we can first solve the first equation for x:

x = y - 4

We can substitute this expression for x into the second equation:

(y - 4) + 8y = 2

Combining like terms, we get:

9y - 4 = 2

Adding 4 to both sides, we get:

9y = 6

Dividing both sides by 9, we get:

y = 6/9 = 2/3

Now that we have the value of y, we can substitute it back into the first equation to find x:

x = (2/3) - 4

Simplifying, we find:

x = -10/3

Therefore, the solution to the system is (x, y) = (-10/3, 2/3), which written as an ordered pair is (-3.33, 0.67). So, the correct answer is:

(-3.33, 0.67)

a b or c