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(23,−313)left parenthesis Start Fraction 2 over 3 End Fraction comma negative 3 Start Fraction 1 over 3 End Fraction right parenthesisno solutionno solutioninfinite solutionsinfinite solutions
To solve the system of equations using the substitution method, we will first solve one equation for one variable and substitute that expression into the second equation.
From the first equation, we have x = y - 4.
Substituting this expression into the second equation, we get (y - 4) + 8y = 2.
Combining like terms, we have 9y - 4 = 2.
Adding 4 to both sides, we get 9y = 6.
Dividing both sides by 9, we find y = 6/9 = 2/3.
Now we substitute this value of y back into the first equation to solve for x.
x = (2/3) - 4 = -12/3 - 4 = -16/3 = -5 1/3.
Therefore, the solution to the system of equations is (x, y) = (-5 1/3, 2/3).
Answer: (-5 1/3, 2/3)