Question

Solve the following pairs of simultaneous equations

73x + 27y = 19 and 27x + 73y= -119​

Answer 1

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$\huge{\mathfrak{\purple{\boxed{\orange{\underbrace{\overbrace{\green{Answer}}}}}}}}$

$\: \: \: \: \: \: \: \blue \bigstar { \bf{solve \: the \: following \: pairs \: of \: simultaneous \: equations}}$

$\: \: \: \: \: \sf{73x + 27y = 19}...........(1)$

$\: \: \: \: 27x + 73y = - 119.......(2)$

$\: \: \: \: \ddag \boxed{ \bf{solve \: this \: equation \: by \: adding \: and \: subtracting}}$

$\: \: \: \: \boxed { \sf \pink{ \ \: by \: adding \: equation \: (1) \: and \: (2) \: we \: get}}$

$\: \: \: \: \dashrightarrow \sf{73x + 27y = 19 .....(1)}$

$\: \: \: \sf27x + 73y = - 119.....(2)$

$\: \: \: \implies \sf{ 100x + 100y = - 100}.......(3) \: by \: adding$

$\: \ \: \: \ \: \star \boxed{ \bf \red{ \: dividing \: each \: term \: by \: 100 \: we \: get}}$

$\: \: \: \ \implies \boxed{ \sf{x + y = - 1.........(3)eqn}}$

$\: \: \: \: \bf{ \: subtracting \: both \: equation \: (1) \: and \: (2) \: we \: get}$

$\: \: \: \dashrightarrow \sf{73x + 27y = 19....(1)}$

$\: \: \: \sf{27x + 73y = - 119...(2)}$

$\: \: \: \: \implies \bf{46x - 46y = 138}$

$\: \: \: \: \star \sf{ \: dividing \: each \: term \: by \: 46}$

$\: \: \: \implies \boxed{ \sf{ \: we \: get \: x - y = 3....(4)eqn}}$

$\: \: \: \: \: \boxed { \rm \pink{now \: solving \: equation \: (3) \: and \: (4) \: to \: get \: x \: and \: y \: values}}$

$\: \: \boxed{ \sf{by \: adding \: equation \: (3) \: and \: (4)}}$

$\: \: \: \dashrightarrow \sf{x + y = - 1.....(3)}$

$\: \: \: \: \sf{x - y = 3.....(4)}$

$\: \: \: \implies \bf{2x = 2}$

$\: \: \: \: \bf{x = \cancel\frac{2}{2} = 1}$

$\: \: \: \: \blue \star \boxed{ \sf{ \: put \: the \: value \: in \: (3) \: or \: (4) \: to \: get \: y \: value}}$

$\: \: \: \implies \sf{1 - y = 3}$

$\: \: \: \implies \sf{1 - y - 3 = 0}$

$\: \: \: \: \implies \sf{ - y - 2 = 0}$

$\: \: \: \: \implies \sf{y = - 2}$

$\: \: \: \: \: \bigstar \boxed { \sf \pink{ \: answer \: will \: be \: x = 1 \: and \: y = - 2}}$

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