If \(4x + 5y = 10\) and \(x + 3y = 8\), then find \(\frac{5x + 8y}{3}\).

A. 18
B. 15
C. 12
D. 9
E. 6

{ x + 3 y = 8 4 x + 5 y = 10 ​ ⇒ { ( − 4 ) x + ( − 4 ) .3 y = ( − 4 ) 8 4 x + 5 y = 10 ​ ⇒ { − 4 x − 12 y = − 32 4 x + 5 y = 10 ​ ⇒ 5 y − 12 y = 10 − 32 ⇒ − 7 y = − 22 ⇒ y = 7 22 ​
y = 7 22 ​ ∧ x + 3 y = 8 ⇒ x + 3. 7 22 ​ = 8 ⇒ − 7 10 ​
3 5 x + 8 y ​ = 3 5 ( − 7 10 ​ ) + 8. 7 22 ​ ​ = 3 − 7 50 ​ + 7 176 ​ ​ = 3 7 126 ​ ​ = 3 18 ​ = 6

Answered by turk3005 | 2024-06-10

\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

Answered by kate200468 | 2024-06-10

By solving the simultaneous equations 4 x + 5 y = 10 and x + 3 y = 8 , we find that x = − 7 10 ​ and y = 7 22 ​ . Substituting these values into 3 5 x + 8 y ​ gives us a final answer of 6 . Thus, the answer is option E: 6.
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Answered by turk3005 | 2024-12-24