Question

Use the substitution method to solve the system x=y-4,x+8y=2.

Answer 1

To solve the system using the substitution method, we need to solve one equation for one variable and then substitute it into the other equation.

First, let's solve the first equation x = y - 4 for x:
x = y - 4

Now, substitute this expression for x in the second equation x + 8y = 2:
(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 y = 2/3 back into the first equation x = y - 4:
x = (2/3) - 4

Multiply 2/3 by 3/3 to have a common denominator:
x = 6/9 - 12/3

Simplify:
x = 6/9 - 36/9
x = -30/9

Simplify the result:
x = -10/3

So the solution to the system is x = -10/3 and y = 2/3.