Math, asked by utssavgarg10, 5 months ago

x/2 + y/3 = 5 and x/2 - y/9 = 6 by Substitution

Answers

Answered by amey0512
1

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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