Question

If 3m +5n =9 and 5m +3n =7 then find the value of 8m +8n.

Answer 1

Given 3m+5n=9 -----(1)

5m+3n=7 -----(3)

multiply eq (1) by 5 and eq (2)by (3) we get

15m+25n=45

15m+9n=21

___________

16n=34. $[n=\frac{17}{8}]$

now form eq (1)

$3m=9-\frac{5\times 17}{8}=\frac{72-85}{8}=\frac{-13}{8}.$

$m=\frac{-13}{24}$

Now $8m+8n=8(m+n)=8(\frac{-13}{24}+\frac{17}{8})=\frac{51-13}{24}$

$[8m+8n=\frac{38}{3}]$