Question

solve the system of equations by the substitution method.\
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$$\begin{cases}5x + 4y = 47\\\\x = 3y - 2\\end{cases}$$

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select the correct choice below and, if necessary, fill in the answer box to complete your choice.\
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\\(\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: Substitute \( x = 3y - 2 \) into \( 5x + 4y = 47 \)

Substitute \( x \) in the first equation with \( 3y - 2 \), we get \( 5(3y - 2) + 4y = 47 \).

Step2: Simplify the equation

Expand the left - hand side: \( 15y-10 + 4y=47 \). Combine like terms: \( 19y-10 = 47 \).

Step3: Solve for \( y \)

Add 10 to both sides: \( 19y=47 + 10=57 \). Then divide both sides by 19: \( y=\frac{57}{19}=3 \).

Step4: Solve for \( x \)

Substitute \( y = 3 \) into \( x = 3y-2 \), we get \( x=3\times3 - 2=9 - 2 = 7 \).

Answer:

A. The solution is \((7, 3)\)