Use the substitution method to solve the system x = y - 4, x + 8y = 2.
• (2/3,-3 1/3)
• (-3 1/3, 2/3)
• infinite solutions
• no solution
To solve the system using the substitution method, we will solve one equation for a variable and then substitute that expression into the other equation.
From the first equation, x = y - 4.
Substitute this expression for x in the second equation:
(y - 4) + 8y = 2.
Simplify the equation:
9y - 4 = 2.
Add 4 to both sides:
9y = 6.
Divide both sides by 9:
y = 6/9.
Simplify the fraction:
y = 2/3.
Now substitute the value of y back into the first equation:
x = (2/3) - 4.
To find a common denominator for the fraction, convert 4 to be 12/3:
x = (2/3) - (12/3).
Simplify the expression:
x = -10/3.
The solution to the system is (-10/3, 2/3).
Therefore, the answer is not one of the given options.