Question

Use the substitution method to solve the system x=y−4 , x+8y=2 . Evaluate and give all possible answers

Answer 1

To solve the system of equations using the substitution method, we'll start with the equations given:

1. \( x = y - 4 \)
2. \( x + 8y = 2 \)

We can substitute the expression for \( x \) from the first equation into the second equation.

Substituting \( x \) in the second equation:

\[
(y - 4) + 8y = 2
\]

Now combine like terms:

\[
y - 4 + 8y = 2
\]
\[
9y - 4 = 2
\]

Next, add 4 to both sides to isolate the term with \( y \):

\[
9y = 2 + 4
\]
\[
9y = 6
\]

Now, divide both sides by 9:

\[
y = \frac{6}{9} = \frac{2}{3}
\]

Now that we have \( y \), we can substitute it back into the first equation to find \( x \):

\[
x = y - 4 = \frac{2}{3} - 4
\]

Converting 4 to a fraction with a denominator of 3:

\[
4 = \frac{12}{3}
\]

So now we have:

\[
x = \frac{2}{3} - \frac{12}{3} = \frac{2 - 12}{3} = \frac{-10}{3}
\]

Thus, the solution to the system of equations is:

\[
x = \frac{-10}{3}, \quad y = \frac{2}{3}
\]

So the final answer is:

\[
\left( x, y \right) = \left( \frac{-10}{3}, \frac{2}{3} \right)
\]