Question

if
$4x + 3y = 10, 3x + 4y =- 3$
then find the value of x + y​

Answer 1

$\tt{\underline{\underline{ \pink{Solution :}}}}$

$\tt \: \purple{3x \: + 4y \: = \: 10} \\ \\\tt \: 3x \: = \: 10 - 4y \\ \\ \tt x \: = \: \frac{10 -4y }{3} \: \: \: \: \: - - - - - 1\\ \\ \tt \: (by \: \: substuting \: \: method) \\ \\ \\ \tt \: now... \\ \\ \tt \: \purple{4x + 3y = 3} \: \: \: - - - - 2 \\ \\ \tt putting \: \: the \: \: value \: \: of \: \: equation \: \: 1 \: \: in \: \: equation \: \: 2. \\ \\ \implies\tt4( \frac{ 10 - 4y}{3} ) + 3y \: = \: - 3 \\ \\ \implies \tt \frac{40 - 4y}{3} + 9y \: = - 3 \\ \\ \implies \tt40 - 7y \: = \: - 9 \\ \\ \implies \tt - 7y \: = \: - 9 - 40 \\ \\ \implies \tt y \: = \: \frac{49}{ - 7} \\ \\ \implies \tt \: \purple{y \: = - 7} \\ \\ \\ \tt \: putting \: \: the \: \: value \: \: of \: \: y \: \: in \: equation \: \: 1. \\ \\ \tt x \: = \: \frac{10 - 4 \times ( - 7)}{3} \\ \\ \tt\: x = \: \frac{10 - 28}{3} \\ \\ \tt x \: = \frac{ - 18}{3} \\ \\ \tt \: x \: = 6 \\ \\ \tt \therefore \: the \: \: value \: \: of \: \: \: x = \: 6 \: \: and \: \: \: \: y \: = \: - 7$

$~~~~~~~~~~~~~~~~~\fbox\pink{x~+~y= 6~+~(-7)~ =~ 1}$

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$\tt{\underline{\underline{ \pink{Answer:}}}}$

$~~~~~~~~~~~~~~~~~~~~\fbox\pink{1}$