Question

Solving Simultaneous Equations Using Substitution Quick Check
2 of 52 of 5 Items
Question
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

no solution
no solution

(23,−313)

Answer 1

To solve the system of equations using substitution, we start with the following equations:

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

First, we will 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:
\[
9y = 6
\]

Now, divide by 9:
\[
y = \frac{6}{9} = \frac{2}{3}
\]

Now that we have \( y \), we can substitute back to find \( x \):
\[
x = y - 4 = \frac{2}{3} - 4
\]
\[
x = \frac{2}{3} - \frac{12}{3} = \frac{2 - 12}{3} = \frac{-10}{3}
\]

Thus, the solution is:
\[
\left( \frac{-10}{3}, \frac{2}{3} \right)
\]

Checking the response options:
- \( (-3 \frac{1}{3}, \frac{2}{3}) \) can be converted to an improper fraction: \( (-\frac{10}{3}, \frac{2}{3}) \).

So the correct response is:
\[
\left( -\frac{10}{3}, \frac{2}{3} \right)
\]

Thus the correct option from your responses is:
\[
(-3 \frac{1}{3}, \frac{2}{3})
\]