Solve the following simultaneous equations. 7 2 x+1 +13 y+2 =27 ; 13 2 x+1 +7 y+2 =33

Let 1 2 x+1 =m and 1 y+2 =n 7 m+13 n=27 (I) 13 m+7 n=33 (II) Adding Eq. I and II 20 m+20 n=60 m+n=3 (III) Subtract Eq. I and II -6 m+6 n=-6 -m+n=-1 (IV) Equating Eq. III and IV m + n =3 - m + n =-1 2 n =2 n =1 Substituting n=1 in Eq. III m +1=3 m=3-1 m=2 1 2 x +1 = m 1 2 x +1 =2 2(2 x +1)=1 4 x +2=1 4 x =1-2 4 x =-1 x =-1 4 1 y +2 = n 1 y +2 =1 y +2=1 y =1-2 y =-1 Hence, ( x , y )= (-1 4 ,-1 )

Solve the following simultaneous equations. 7 2 x+1 +13 y+2 =27 ;…

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Question

Solve the following simultaneous equations.
$\frac{7}{2 x+1}+\frac{13}{y+2}=27 ; \frac{13}{2 x+1}+\frac{7}{y+2}=33$

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Answer

Let $\frac{1}{2 x+1}=m$ and $\frac{1}{y+2}=n 7 m+13 n=27 \ldots(I)$
$13 m+7 n=33\dots(II)$
Adding Eq. I and II
$20 m+20 n=60 \Rightarrow m+n=3 \ldots \text { (III) }$
Subtract Eq. I and II
$-6 m+6 n=-6 \Rightarrow-m+n=-1 \ldots(IV)$
Equating Eq. III and IV
$m + n =3 $
$\underline{ - m + n =-1} $
$2 n =2 $
$n =1$
Substituting $n=1$ in Eq. III
$m +1=3 $
$m=3-1 $
$m=2 $
$\therefore \frac{1}{2 x +1}= m \Rightarrow \frac{1}{2 x +1}=2 \Rightarrow 2(2 x +1)=1 \Rightarrow 4 x +2=1 \Rightarrow 4 x =1-2 $
$\Rightarrow 4 x =-1 \Rightarrow x =-\frac{1}{4} $
$\therefore \frac{1}{ y +2}= n \Rightarrow \frac{1}{ y +2}=1 \Rightarrow y +2=1 \Rightarrow y =1-2 \Rightarrow y =-1 $
$\text { Hence, }( x , y )=\left(-\frac{1}{4},-1\right)$