Answer:
[tex]x=8\frac34\ \,,\quad y=8\frac12[/tex]
Step-by-step explanation:
[tex]\Delta TRS\sim \Delta LJK \quad\implies\quad \dfrac{|TR|}{|LJ|}=\dfrac{|RS|}{|JK|}=\dfrac{|ST|}{|KL|}\\\\\dfrac{4}{7}=\dfrac{5}{x}=\dfrac{6}{y+2}\\\\\\\dfrac{4}{7}=\dfrac{5}{x}\quad\implies\quad4x=5\cdot7\quad\implies\quad x=\dfrac{35}4=8\frac34\\\\\\\dfrac{5}{x}=\dfrac{6}{y+2}\quad\implies\quad 5(y+2)=6\cdot\dfrac{35}4\\\\5y+10=3\cdot\dfrac{35}2\\\\5y\ =\ \dfrac{3\cdot35}2-10\\ \div5\qquad\quad \div5\\\\y=\dfrac{3\cdot7}2-2=10\frac12-2=8\frac12[/tex]
