x/2 + y/3 = 5 and x/2 - y/9 = 6 by Substitution
Answers
Answer:
Step-by-step explanation:
\begin{gathered} Given\:pair\:of\: equations:\\\frac{x}{7}+\frac{y}{3}=5\end{gathered}
Givenpairofequations:
7
x
+
3
y
=5
\implies \frac{y}{3}=5-\frac{x}{7}\:---(1)⟹
3
y
=5−
7
x
−−−(1)
and\:\frac{x}{2}-\frac{y}{9}=6and
2
x
−
9
y
=6
\implies \frac{x}{2}-\frac{y}{3}\times \frac{1}{3}=6\:---(2)⟹
2
x
−
3
y
×
3
1
=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)⟹
2
x
−(5−
7
x
)×
3
1
=6−−−(2)
\implies \frac{x}{2}-\frac{5}{3}+\frac{x}{21}=6⟹
2
x
−
3
5
+
21
x
=6
\implies \frac{x}{2}+\frac{x}{21}=6+\frac{5}{3}⟹
2
x
+
21
x
=6+
3
5
\implies \frac{21x+2x}{42}=\frac{18+5}{3}⟹
42
21x+2x
=
3
18+5
\implies \frac{23x}{42}=\frac{21}{3}⟹
42
23x
=
3
21
\implies x = \frac{23}{3}\times \frac{42}{23}⟹x=
3
23
×
23
42
\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}
3
y
=5−
7
14
\implies \frac{y}{3}=5-2⟹
3
y
=5−2
\implies y = 3\times 3 = 9⟹y=3×3=9
Therefore,
x = 14 , \: y = 9x=14,y=9
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