Question

solve the system of equations by the substitution method.
\

$$\begin{cases} x + 8y = 13 \\\\ 3x + 5y = 1 \\end{cases}$$

select the correct choice below and, if necessary, fill in the answer box to complete your choice

\bigcirc a. the solution is \square. (simplify your answer. type an ordered pair)
\bigcirc b. there are infinitely many solutions.
\bigcirc c. there is no solution.

Explanation:

Step1: Solve for x in first equation

From \( x + 8y = 13 \), we get \( x = 13 - 8y \).

Step2: Substitute x into second equation

Substitute \( x = 13 - 8y \) into \( 3x + 5y = 1 \):
\( 3(13 - 8y) + 5y = 1 \)
Expand: \( 39 - 24y + 5y = 1 \)
Simplify: \( 39 - 19y = 1 \)
Subtract 39: \( -19y = -38 \)
Divide: \( y = 2 \).

Step3: Find x using y=2

Substitute \( y = 2 \) into \( x = 13 - 8y \):
\( x = 13 - 8(2) = 13 - 16 = -3 \).

Answer:

A. The solution is \((-3, 2)\)