Selesaikan sistem persamaan dengan metode eliminasi 3x+2y -12= 0 dan

Berikut ini adalah pertanyaan dari hanaalyaf9193 pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Pertama

Selesaikan sistem persamaan dengan metode eliminasi 3x+2y -12= 0 dan 5x-3y =21

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

$\mathbb \color{aqua} \underbrace{JAWABAN}$

$\small \boxed{ \bold{x = 4 \frac{2}{19}} }$

$\small \boxed{ \sf\bold{y = - \frac{3}{19} }}$

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$\mathbb \color{orange} \underbrace{PENYELESAIAN}$

Persamaan (1)

$\sf 3x + 2y - 12 = 0~~~~~~~~~~~ \\ \sf3x + 2y = 12 \\$

Persamaan (2)

$\sf 5x - 3y = 21 \\$

Eliminasi : y

$\sf 3x + 2y = 12~~~ | \times 3| ~~~~~9x + \cancel{ 6y} = 36~~~~~~ \\ \sf 5x - 3y = 21~~~ | \times 2|~~~ 10x - \cancel{6y} = 42~~~~~~ \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\underline{~~~~~~~~~~~~~~~~~~~~~~~~~} + \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \sf 19x = 78~~~~~~ \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \sf x = \frac{78}{19} ~~~~~ \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \sf x = 4 \frac{2}{19} ~~~ \\$

Eliminasi : x

$\sf 3x + 2y = 12~~~ | \times 5| ~~~\cancel{15x} + 10y = 60~~~~~~ \\ \sf 5x - 3y = 21~~~ | \times 3|~~~ \cancel{15x} - ~~9y = 63~~~~~~ \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\underline{~~~~~~~~~~~~~~~~~~~~~~~~~} - \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \sf 19y = - 3~~~~~~ \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \sf y = \frac{ - 3}{19} ~~~~~ \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \sf y = - \frac{3}{19} ~~~ \\$

$\small \boxed{ \bold{HP = \{x = 4 \frac{2}{19} \: , \: y = - \frac{3}{19} \}}}$

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$\mathbb \color{violet} \underbrace{PEMBUKTIAN}$

=> menggunakan metode substitusi

$\sf 3x + 2y - 12 = 0~~~~~~~~~~~~~~~~~~~~ \\ \sf 3(4 \frac{2}{19} ) + 2( - \frac{3}{19} ) - \frac{12}{1} = 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \sf 3( \frac{78}{19} ) - \frac{6}{19} - \frac{12}{1} = 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \sf \frac{234}{19} - \frac{6}{19} - \frac{228}{19} = 0~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \sf \frac{234 - 6 - 228}{19} = 0~~~~~~~~~~~~~~~~~~~~~~~~ \\ \sf \frac{0}{19} = 0~~~~ \\ \sf0 = 0~ \\$

----------atau----------

$\\ \sf5x-3y =21~~~~~~~~~~~ \\ \sf5(4 \frac{2}{19} ) - 3( - \frac{3}{19} ) = 21~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \sf5( \frac{78}{19} ) + \frac{9}{19} = 21 ~~~~~~~~~~~~~~~~~\\ \sf \frac{390}{19} + \frac{9}{19} = 21 ~~~~~~~~~~~~~\\ \sf \frac{390 + 9}{19} = 21~~~~~~~~~~ \\ \sf \frac{399}{19} = 21~~~ \\ \sf \frac{21}{1} = 21~ \\ \sf21 = 21$