Question

If 4x + 5y =10 and x + 3y = 8, then (5x+8y)/3

(A) 18
(B) 15
(C) 12
(D) 9
(E) 6

Answer 1

`\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= (22)/(7)`


`y= (22)/(7) \wedge x+3y=8\Rightarrow \\ \\ x+3.(22)/(7)=8\Rightarrow - (10)/(7)`


`(5x+8y)/(3) = \\ \\ (5(- (10)/(7))+8.(22)/(7))/(3) = \\ \\ ( -(50)/(7)+ (176)/(7))/(3)= \\ \\ ( (126)/(7))/(3) = (18)/(3)=6`

Answer 2

`\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`