Answer
\[\left\{ {\left( {2,0} \right)} \right\}\]
Work Step by Step
\[\begin{gathered}
\left\{ {\begin{array}{*{20}{c}}
{5x + 4y = 10} \\
{3x - 7y = 6}
\end{array}} \right. \hfill \\
{\text{Given the system}} \hfill \\
\left\{ {\begin{array}{*{20}{c}}
{{a_1}x + {b_1}y = {c_1}} \\
{{a_2}x + {b_2}y = {c_2}}
\end{array}} \right. \hfill \\
D = \left| {\begin{array}{*{20}{c}}
{{a_1}}&{{b_1}} \\
{{a_2}}&{{b_2}}
\end{array}} \right|,\,\,\,{D_x} = \left| {\begin{array}{*{20}{c}}
{{c_1}}&{{b_1}} \\
{{c_2}}&{{b_2}}
\end{array}} \right|,\,\,{D_y} = \left| {\begin{array}{*{20}{c}}
{{a_1}}&{{c_1}} \\
{{a_2}}&{{c_2}}
\end{array}} \right| \hfill \\
{\text{First find }}D,{\text{ If }}D \ne 0,\,{\text{ then find }}{D_x}{\text{ and }}{D_y} \hfill \\
D = \left| {\begin{array}{*{20}{c}}
5&4 \\
3&{ - 7}
\end{array}} \right| = - 35 - 12 = - 47 \hfill \\
{D_x} = \left| {\begin{array}{*{20}{c}}
{10}&4 \\
6&{ - 7}
\end{array}} \right| = - 70 - 24 = - 94 \hfill \\
{D_y} = \left| {\begin{array}{*{20}{c}}
5&{10} \\
3&6
\end{array}} \right| = 30 - 30 = 0 \hfill \\
{\text{Using the Cramer's rule}} \hfill \\
x = \frac{{{D_x}}}{D} = \frac{{ - 94}}{{ - 47}} = 2,\,\,\,\,\,\,\,\,\,y = \frac{{{D_y}}}{D} = \frac{0}{{ - 47}} = 0 \hfill \\
{\text{The solution set is}} \hfill \\
\left\{ {\left( {2,0} \right)} \right\} \hfill \\
\end{gathered} \]
