Use the substitution method to solve the system x=y-4,x+8y=2.
(-3(1/3),2/3)
no solution
infinite solutions
(2/3,-3(1/3))
To solve the system of equations using the substitution method, we start with the first equation:
x = y - 4
Now substitute this expression for x in 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 to solve for y:
y = 6/9
Simplify the fraction:
y = 2/3
Now substitute this value of y back into the first equation to solve for x:
x = (2/3) - 4
To simplify, convert 4 to a fraction with the same denominator as 2/3:
x = (2/3) - (12/3)
x = -10/3
Therefore, the solution to the system of equations is (x, y) = (-10/3, 2/3).