Question

_ +_=8
+ +
__. _=6
13. 8

Answer 1

$\underline{\underline{\Huge{\textbf{Question:}}}}$

$\begin{large}\begin{array}{ccccc}\underline{~~~}&+&\underline{~~~}&=8\\+&&+&&\\\underline{~~~}&-&\underline{~~~}&=6\\\shortparallel&&\shortparallel\\13&&8\end{array}\end{large}$




$\underline{\underline{\Huge{\textbf{Solution:}}}}$

$\underline{\Large{\textbf{Step-1:}}}$
$\sf\textsf{Assume variables for empty blanks.}$

$\begin{large}\begin{array}{ccccc}\underline{~\sf A~}&+&\underline{~ \sf B~}&=8\\+&&+&&\\\underline{~\sf C~}&-&\underline{~\sf D~}&=6\\\shortparallel&&\shortparallel\\13&&8\end{array}\end{large}$



$\underline{\Large{\textbf{Step-2:}}}$
$\sf\textsf{Form Set of Equations using}\\\sf\textsf{the variables considered}$

$\begin{array}{cl@{\cdots\cdot}r}\sf A+B &= \sf 8&[1]\\\\\sf C-D &= \sf 6\quad &[2]\\\\\sf A+C &= \sf 13&[3]\\\\\sf B+D &= \sf 8 &[4]\end{array}$

Here, we have 4 equations and 4 variables.

$\textbf{To solve for 4 variables,}\\\textbf{4 distinct equations are needed.}$

We have the sufficient data to solve.



$\underline{\Large{\textbf{Step-3:}}}$
$\sf\textsf{Solve the Equations to obtain}\\\sf\textsf{value of variables}$


From [1] & [4]

$\begin{aligned}\sf A+B &= B+D\\\\\implies \sf A-D &= B-B\\\\\implies \sf A-D&=0\end{aligned}$

$\implies A = D$ ———[5]


Substitute in [3]

$\implies \sf C+D = 13$ ———[6]


Do [6]-[2]

$\begin{array}{cccccccc}&C&+&&D&=&&13\\&C&-&&D&=&&6 \\-&&&+&&&-&\\&&&&2D&=&&7\end{array}$

$\implies \sf D = \dfrac {7}{2}$


From [5]

$\implies \sf A = \dfrac{7}{2}$


Substitute A in [1]

$\begin{aligned}\implies \sf \dfrac{7}{2} + B &= 8\\\\\implies \sf B &= 8-\dfrac{7}{2}\\\\ \implies \sf B &= \dfrac{16-7}{2}\\\\ \implies \sf B &= \dfrac{9}{2}\end{aligned}$


Substitute B in [3]

$\begin{aligned}\implies \sf \dfrac{7}{2} +C &= 13\\\\\implies \sf C &= 13-\dfrac{7}{2}\\\\\implies \sf C &= \dfrac{26-7}{2}\\\\\implies \sf C &= \dfrac{11}{2}\end{aligned}$



$\underline{\Large{\textbf{Step-4:}}}$
$\sf\textsf{Fill the blanks with obtained value}\\\sf\textsf{of variables}$


$\sf A = D = \dfrac{7}{2} = 3.5\\\\\sf B = \dfrac{9}{2} = 4.5\\\\\sf C = \dfrac{19}{2}$

$\therefore$

$\begin{Large}\begin{array}{ccccc}\underline{~3.5~}&+&\underline{~4.5~}&=8\\+&&+&&\\\underline{~9.5~}&-&\underline{~3.5~}&=6\\\shortparallel&&\shortparallel\\13&&8\end{array}\end{Large}$

Answer 2

Answer:

Hope it helps you.......