Use the substitution method to solve the system x=y−4 , x+8y=2 .(1 point)
Responses
infinite solutions
infinite solutions
(−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 parenthesis
no solution
To solve the system using the substitution method, we can first solve one equation for a variable and substitute it into the other equation.
From the first equation, we have x = y - 4.
Substitute this expression for x into 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 = 6/9
Simplify:
y = 2/3
Now substitute this value for y back into the first equation:
x = (2/3) - 4
x = 2/3 - 12/3
x = -10/3
Therefore, the solution to the system is (-10/3, 2/3).