Question

solve the system of equations by the substitution method.\

$$\begin{cases}3x + 9y = 18\\\\6x + 18y = 42\\end{cases}$$

\select the correct choice below and fill in any answer boxes within your choice.\
\bigcirc a. there is one solution. 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: Simplify the first equation

Divide the first equation \(3x + 9y = 18\) by 3:
\(\frac{3x}{3}+\frac{9y}{3}=\frac{18}{3}\)
\(x + 3y = 6\)
We can express \(x\) in terms of \(y\): \(x = 6 - 3y\)

Step2: Substitute \(x = 6 - 3y\) into the second equation

The second equation is \(6x + 18y = 42\). Substitute \(x\):
\(6(6 - 3y)+18y = 42\)
Expand the left - hand side: \(36-18y + 18y = 42\)
Simplify the left - hand side: \(36=42\)

Answer:

C. There is no solution.