Question

solve the system of equations by the substitution method.\
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$$\begin{cases}x + 7y = 18\\\\2x + 3y = 3\\end{cases}$$

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

Explanation:

Step1: Solve the first equation for x

From \( x + 7y = 18 \), we can express \( x \) in terms of \( y \) as \( x = 18 - 7y \).

Step2: Substitute x into the second equation

Substitute \( x = 18 - 7y \) into \( 2x + 3y = 3 \). We get \( 2(18 - 7y) + 3y = 3 \).

Step3: Simplify and solve for y

First, expand the left - hand side: \( 36-14y + 3y=3 \).
Combine like terms: \( 36-11y = 3 \).
Subtract 36 from both sides: \( - 11y=3 - 36=-33 \).
Divide both sides by - 11: \( y=\frac{-33}{-11} = 3 \).

Step4: Substitute y = 3 back into the expression for x

We know that \( x = 18-7y \), substitute \( y = 3 \) into it: \( x=18-7\times3=18 - 21=-3 \).

Answer:

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