Answer
$\{(4,2)\}$
Work Step by Step
Multiplying the first equation by $5$ and the second equation by $3$, the given system, $
\begin{array}{l}
5x-3y=14
\\
2x+5y=18
\end{array}$, is equivalent to
\begin{align*}\require{cancel}
25x-15y&=70
\\
6x+15y&=54
.\end{align*}
Adding the two equations above and solving for the variable result to
\begin{align*}\require{cancel}
31x&=124
\\\\
\dfrac{\cancel{31}x}{\cancel{31}}&=\dfrac{124}{31}
\\\\
x&=4
.\end{align*}
Substituting $x=4$ in the first equation, $
5x-3y=14
$, results to
\begin{align*}\require{cancel}
5(4)-3y&=14
\\
20-3y&=14
\\
20-14&=3y
\\
6&=3y
\\\\
\dfrac{6}{3}&=\dfrac{\cancel3y}{\cancel3}
\\\\
2&=y
.\end{align*}
Hence, the solution set of the system $\begin{array}{l}
5x-3y=14
\\
2x+5y=18
\end{array}$ is $
\{(4,2)\}
$.
