TUGAS MATEMATIKA Selesaikan SPLOV dibawah ini dengan menggunakan metode eliminasi,

Berikut ini adalah pertanyaan dari alvyanasari pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Atas

TUGAS MATEMATIKA Selesaikan SPLOV dibawah ini dengan menggunakan metode eliminasi, substitusi dan gaburgan !1. x-2y = 5
2 x + y = 11
2. 5x + 2y = 2
3x+y=2

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

Metode enliminasi :

x - 2y = 5 x - 2y = 5 |×1| x - 2y = 5

x + y = 11 - x + y = 11 + |×2| 2x + 2y = 22 +

------------- ---------------- --------------------

-3y = -6 3x = 27

y = 2 x = 9

5x + 2y = 2 |×1| 5x + 2y = 2 5x + 2y = 2 |×3| 15x + 6y = 6

3x + y = 2 - |×2| 6x + 2y = 4 - 3x + y = 2 - |×5| 15x + 5y = 10 -

---------------- ---------------- -------------- ------------------

-x = -2 y = -4

x = 2

Metode substitusi :

x = 2y + 5 (1) x - 2y = 5 (3)

x + y = 11 (2) y = -x + 11 (4)

Sub (1) ke (2) Sub (4) ke (3)

2y + 5 + y = 11 x - 2(-x + 11) = 5

3y + 5 = 11 x + 2x -22 = 5

3y = 6 3x = 28

y = 2 x = 9

5x + 2y = 2 (1) 5x + 2y = 2 (3)

y = -3x + 2 (2) x = $- \frac{1}{3} \ y +\ \frac{2}{3}$ (4)

Sub (2) ke (1) Sub (4) ke (3)

5x + 2(-3x +2) = 2 5 $(- \frac{1}{3} \ y +\ \frac{2}{3})$ + 2y = 2

5x - 6x + 4 = 2 $- \frac{5}{3} \ y +\ \frac{10}{3}$ + 2y = 2

-x = -2 $\frac{1}{3} y$ = $-\frac{4}{3}$

x = 2 y = -4

Metode gabungan :

x - 2y = 5 (1)

x + y = 11 (2) -

-----------------

-3y = -6

y = 2 (3)

Sub (3) ke (2)
x + 2 = 11

x = 9

5x + 2y = 2 (1) |×1| 5x + 2y = 2

3x + y = 2 (2) - |×2| 6x + 2y = 4 -

------------------- ----------------

-x = -2

x = 2 (3)

Sub (3) ke (2)

3 * 2 + y = 2

6 + y = 2

y = -4

$Metode enliminasi :1.x - 2y = 5 x - 2y = 5 |×1| x - 2y = 5x + y = 11 - x + y = 11 + |×2| 2x + 2y = 22 + ------------- ---------------- ---------------------3y = -6 3x = 27y = 2 x = 92. 5x + 2y = 2 |×1| 5x + 2y = 2 5x + 2y = 2 |×3| 15x + 6y = 63x + y = 2 - |×2| 6x + 2y = 4 - 3x + y = 2 - |×5| 15x + 5y = 10 - ---------------- ---------------- -------------- ------------------ -x = -2 y = -4 x = 2 Metode substitusi :1.x = 2y + 5 (1) x - 2y = 5 (3)x + y = 11 (2) y = -x + 11 (4)Sub (1) ke (2) Sub (4) ke (3)2y + 5 + y = 11 x - 2(-x + 11) = 53y + 5 = 11 x + 2x -22 = 53y = 6 3x = 28y = 2 x = 92.5x + 2y = 2 (1) 5x + 2y = 2 (3)y = -3x + 2 (2) x = [tex]- \frac{1}{3} \ y +\ \frac{2}{3}[/tex] (4)Sub (2) ke (1) Sub (4) ke (3)5x + 2(-3x +2) = 2 5[tex](- \frac{1}{3} \ y +\ \frac{2}{3})[/tex] + 2y = 25x - 6x + 4 = 2 [tex]- \frac{5}{3} \ y +\ \frac{10}{3}[/tex] + 2y = 2-x = -2 [tex]\frac{1}{3} y[/tex] = [tex]-\frac{4}{3}[/tex]x = 2 y = -4Metode gabungan :1.x - 2y = 5 (1) x + y = 11 (2) - ------------------3y = -6 y = 2 (3)Sub (3) ke (2)x + 2 = 11x = 92. 5x + 2y = 2 (1) |×1| 5x + 2y = 2 3x + y = 2 (2) - |×2| 6x + 2y = 4 - ------------------- ---------------- -x = -2 x = 2 (3)Sub (3) ke (2)3 * 2 + y = 26 + y = 2y = -4$ $Metode enliminasi :1.x - 2y = 5 x - 2y = 5 |×1| x - 2y = 5x + y = 11 - x + y = 11 + |×2| 2x + 2y = 22 + ------------- ---------------- ---------------------3y = -6 3x = 27y = 2 x = 92. 5x + 2y = 2 |×1| 5x + 2y = 2 5x + 2y = 2 |×3| 15x + 6y = 63x + y = 2 - |×2| 6x + 2y = 4 - 3x + y = 2 - |×5| 15x + 5y = 10 - ---------------- ---------------- -------------- ------------------ -x = -2 y = -4 x = 2 Metode substitusi :1.x = 2y + 5 (1) x - 2y = 5 (3)x + y = 11 (2) y = -x + 11 (4)Sub (1) ke (2) Sub (4) ke (3)2y + 5 + y = 11 x - 2(-x + 11) = 53y + 5 = 11 x + 2x -22 = 53y = 6 3x = 28y = 2 x = 92.5x + 2y = 2 (1) 5x + 2y = 2 (3)y = -3x + 2 (2) x = [tex]- \frac{1}{3} \ y +\ \frac{2}{3}[/tex] (4)Sub (2) ke (1) Sub (4) ke (3)5x + 2(-3x +2) = 2 5[tex](- \frac{1}{3} \ y +\ \frac{2}{3})[/tex] + 2y = 25x - 6x + 4 = 2 [tex]- \frac{5}{3} \ y +\ \frac{10}{3}[/tex] + 2y = 2-x = -2 [tex]\frac{1}{3} y[/tex] = [tex]-\frac{4}{3}[/tex]x = 2 y = -4Metode gabungan :1.x - 2y = 5 (1) x + y = 11 (2) - ------------------3y = -6 y = 2 (3)Sub (3) ke (2)x + 2 = 11x = 92. 5x + 2y = 2 (1) |×1| 5x + 2y = 2 3x + y = 2 (2) - |×2| 6x + 2y = 4 - ------------------- ---------------- -x = -2 x = 2 (3)Sub (3) ke (2)3 * 2 + y = 26 + y = 2y = -4$ $Metode enliminasi :1.x - 2y = 5 x - 2y = 5 |×1| x - 2y = 5x + y = 11 - x + y = 11 + |×2| 2x + 2y = 22 + ------------- ---------------- ---------------------3y = -6 3x = 27y = 2 x = 92. 5x + 2y = 2 |×1| 5x + 2y = 2 5x + 2y = 2 |×3| 15x + 6y = 63x + y = 2 - |×2| 6x + 2y = 4 - 3x + y = 2 - |×5| 15x + 5y = 10 - ---------------- ---------------- -------------- ------------------ -x = -2 y = -4 x = 2 Metode substitusi :1.x = 2y + 5 (1) x - 2y = 5 (3)x + y = 11 (2) y = -x + 11 (4)Sub (1) ke (2) Sub (4) ke (3)2y + 5 + y = 11 x - 2(-x + 11) = 53y + 5 = 11 x + 2x -22 = 53y = 6 3x = 28y = 2 x = 92.5x + 2y = 2 (1) 5x + 2y = 2 (3)y = -3x + 2 (2) x = [tex]- \frac{1}{3} \ y +\ \frac{2}{3}[/tex] (4)Sub (2) ke (1) Sub (4) ke (3)5x + 2(-3x +2) = 2 5[tex](- \frac{1}{3} \ y +\ \frac{2}{3})[/tex] + 2y = 25x - 6x + 4 = 2 [tex]- \frac{5}{3} \ y +\ \frac{10}{3}[/tex] + 2y = 2-x = -2 [tex]\frac{1}{3} y[/tex] = [tex]-\frac{4}{3}[/tex]x = 2 y = -4Metode gabungan :1.x - 2y = 5 (1) x + y = 11 (2) - ------------------3y = -6 y = 2 (3)Sub (3) ke (2)x + 2 = 11x = 92. 5x + 2y = 2 (1) |×1| 5x + 2y = 2 3x + y = 2 (2) - |×2| 6x + 2y = 4 - ------------------- ---------------- -x = -2 x = 2 (3)Sub (3) ke (2)3 * 2 + y = 26 + y = 2y = -4$ $Metode enliminasi :1.x - 2y = 5 x - 2y = 5 |×1| x - 2y = 5x + y = 11 - x + y = 11 + |×2| 2x + 2y = 22 + ------------- ---------------- ---------------------3y = -6 3x = 27y = 2 x = 92. 5x + 2y = 2 |×1| 5x + 2y = 2 5x + 2y = 2 |×3| 15x + 6y = 63x + y = 2 - |×2| 6x + 2y = 4 - 3x + y = 2 - |×5| 15x + 5y = 10 - ---------------- ---------------- -------------- ------------------ -x = -2 y = -4 x = 2 Metode substitusi :1.x = 2y + 5 (1) x - 2y = 5 (3)x + y = 11 (2) y = -x + 11 (4)Sub (1) ke (2) Sub (4) ke (3)2y + 5 + y = 11 x - 2(-x + 11) = 53y + 5 = 11 x + 2x -22 = 53y = 6 3x = 28y = 2 x = 92.5x + 2y = 2 (1) 5x + 2y = 2 (3)y = -3x + 2 (2) x = [tex]- \frac{1}{3} \ y +\ \frac{2}{3}[/tex] (4)Sub (2) ke (1) Sub (4) ke (3)5x + 2(-3x +2) = 2 5[tex](- \frac{1}{3} \ y +\ \frac{2}{3})[/tex] + 2y = 25x - 6x + 4 = 2 [tex]- \frac{5}{3} \ y +\ \frac{10}{3}[/tex] + 2y = 2-x = -2 [tex]\frac{1}{3} y[/tex] = [tex]-\frac{4}{3}[/tex]x = 2 y = -4Metode gabungan :1.x - 2y = 5 (1) x + y = 11 (2) - ------------------3y = -6 y = 2 (3)Sub (3) ke (2)x + 2 = 11x = 92. 5x + 2y = 2 (1) |×1| 5x + 2y = 2 3x + y = 2 (2) - |×2| 6x + 2y = 4 - ------------------- ---------------- -x = -2 x = 2 (3)Sub (3) ke (2)3 * 2 + y = 26 + y = 2y = -4$

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Last Update: Wed, 17 May 23

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