Question

solve the system of equations using the substitution method.
\

$$\begin{cases} x + y = 8 \\\\ x = 3y \\end{cases}$$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\bigcirc a. the solution of the system is \square. (type an ordered pair.)
\bigcirc b. there are infinitely many solutions.
\bigcirc c. there is no solution.

Explanation:

Step1: Substitute \( x = 3y \) into \( x + y = 8 \)

Substitute \( x \) in the first equation with \( 3y \), we get \( 3y + y = 8 \).

Step2: Solve for \( y \)

Combine like terms: \( 4y = 8 \). Then divide both sides by 4: \( y = \frac{8}{4} = 2 \).

Step3: Solve for \( x \)

Substitute \( y = 2 \) into \( x = 3y \), we get \( x = 3\times2 = 6 \).

Answer:

A. The solution of the system is \( (6, 2) \).