Question

solve the system of equations by the substitution method.
\

$$\begin{cases} x + y = 18 \\\\ y = -4x \\end{cases}$$

select the correct choice 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: Substitute \( y = -4x \) into \( x + y = 18 \)

Substitute \( y \) in the first equation with \( -4x \), we get \( x + (-4x) = 18 \).

Step2: Simplify and solve for \( x \)

Simplify the left side: \( x - 4x = -3x \), so the equation becomes \( -3x = 18 \). Divide both sides by \( -3 \): \( x = \frac{18}{-3} = -6 \).

Step3: Substitute \( x = -6 \) into \( y = -4x \)

Substitute \( x = -6 \) into \( y = -4x \), we get \( y = -4\times(-6) = 24 \).

Answer:

A. The solution is \((-6, 24)\)