Answer :
[tex] \left \{ {{4x + 5y =10} \atop {x + 3y = 8}} \right. \Rightarrow \\ \\ \left \{ {{4x + 5y =10} \atop {(-4)x + (-4).3y = (-4)8}} \right. \Rightarrow \\ \\ \left \{ {{4x + 5y =10} \atop {-4x -12y = -32}} \right. \Rightarrow \\ \\ \\ 5y-12y=10-32 \Rightarrow \\ \\ -7y=-22\Rightarrow \\ \\ y= \frac{22}{7} [/tex]
[tex]y= \frac{22}{7} \wedge x+3y=8\Rightarrow \\ \\ x+3.\frac{22}{7}=8\Rightarrow - \frac{10}{7} [/tex]
[tex] \frac{5x+8y}{3} = \\ \\ \frac{5(- \frac{10}{7})+8.\frac{22}{7}}{3} = \\ \\ \frac{ -\frac{50}{7}+ \frac{176}{7}}{3}= \\ \\ \frac{ \frac{126}{7}}{3} = \frac{18}{3}=6 [/tex]
[tex]y= \frac{22}{7} \wedge x+3y=8\Rightarrow \\ \\ x+3.\frac{22}{7}=8\Rightarrow - \frac{10}{7} [/tex]
[tex] \frac{5x+8y}{3} = \\ \\ \frac{5(- \frac{10}{7})+8.\frac{22}{7}}{3} = \\ \\ \frac{ -\frac{50}{7}+ \frac{176}{7}}{3}= \\ \\ \frac{ \frac{126}{7}}{3} = \frac{18}{3}=6 [/tex]
[tex] \left \{{ \big{4x + 5y =10} \atop \big{x + 3y = 8}} \right.\\-----------\\4x+5y+x+3y=10+8\\5x+8y=18\\\\ \frac{\big{ 5x+8y}}{\big{3}}=\frac{\big{ 18}}{\big{3}}=6\ \ \ \Rightarrow\ \ \ Ans.\ E[/tex]
