[tex]\begin{gathered} \text{Let:} \\ 5x-3y=4\text{ (1)} \\ 7x-2y=4\text{ (2)} \\ \text{Multiply (2) by -3/2:} \\ -\frac{21x}{2}+3y=-6\text{ (3)} \\ (1)+(3) \\ 5x-\frac{21x}{2}-3y+3y=4-6 \\ -\frac{11x}{2}=-2 \\ \text{Solve for x:} \\ -11x=-4 \\ x=-\frac{4}{-11}=\frac{4}{11} \\ \text{ Replace x into (1)} \\ 5(\frac{4}{11})-3y=4 \\ \frac{20}{11}-3y=4 \\ \text{Solving for y:} \\ -3y=4-\frac{20}{11} \\ -3y=\frac{24}{11} \\ y=-\frac{1}{3}\frac{24}{11}=-\frac{8}{11} \end{gathered}[/tex]
