x/7 + y/3 = 5 ; x/2 - y/9 = 6 .solve for x and y
Answers
Answer:
x = 14 , \: y = 9x=14,y=9
Step-by-step explanation:
\begin{gathered} Given\:pair\:of\: equations:\\\frac{x}{7}+\frac{y}{3}=5\end{gathered}Givenpairofequations:7x+3y=5
\implies \frac{y}{3}=5-\frac{x}{7}\:---(1)⟹3y=5−7x−−−(1)
and\:\frac{x}{2}-\frac{y}{9}=6and2x−9y=6
\implies \frac{x}{2}-\frac{y}{3}\times \frac{1}{3}=6\:---(2)⟹2x−3y×31=6−−−(2)
substitute \:(1)\:in \: equation\:(2),\: we\:getsubstitute(1)inequation(2),weget
\implies \frac{x}{2}-(5-\frac{x}{7})\times \frac{1}{3}=6\:---(2)⟹2x−(5−7x)×31=6−−−(2)
\implies \frac{x}{2}-\frac{5}{3}+\frac{x}{21}=6⟹2x−35+21x=6
\implies \frac{x}{2}+\frac{x}{21}=6+\frac{5}{3}⟹2x+21x=6+35
\implies \frac{21x+2x}{42}=\frac{18+5}{3}⟹4221x+2x=318+5
\implies \frac{23x}{42}=\frac{21}{3}⟹4223x=321
\implies x = \frac{23}{3}\times \frac{42}{23}⟹x=323×2342
\implies x = 14\:--(3)⟹x=14−−(3)
\begin{gathered}put \: x=14 \: in \: equation \:(1),\\we\:get\end{gathered}putx=14inequation(1),weget
\frac{y}{3}=5-\frac{14}{7}3y=5−714
\implies \frac{y}{3}=5-2⟹3y=5−2
\implies y = 3\times 3 = 9⟹y=3×3=9
Therefore,
x = 14 , \: y = 9x=14,y=9
•••♪
Answer:
x = 14 , y = 9
Step-by-step explanation:
