tentukan hp dari x= 8/9 y + 1. y = 8/7x-8

jawab

x = 8/9  y + 1 --->kali 9
9x = 8y + 9
9x - 8y = 9

y = 8/7 x - 8 ---> kali 7
7y = 8x - 56
8x -7y = 56

9x - 8y = 9 ...kali 8
8x - 7y = 56..kali 9

72 x- 64 y = 72
72 x- 63 y =504
-y =- 432
y = 432

x = 8/9 (y) - 1
x = 8/9(432) - 1
x = 383

HP (x,y) =(383, 432)

Metode Substitusi :

[tex]x= \frac{8}{9} y + 1 ....(1)\\ \\ y= \frac{8}{7} x-8 ....(2)\\ \\ Substitusikan\ (1)\ ke\ (2)\\ \\y=(\frac{8}{7} \times (\frac{8}{9} y + 1)) -8\\ \\ y= \frac{64}{63}y + \frac{8}{7}-8 \\ \\y- \frac{64}{63}y= \frac{8}{7}-8\\ \\ \frac{63}{63}y- \frac{64}{63}y = \frac{8}{7}-\frac{56}{7} \\ \\ -\frac{1}{63}y= -\frac{48}{7} \\ \\y= -\frac{48}{7} \times (-63) \\ \\ y= (-48) \times (-9) \\ \\ y=432 \\ \\ \\x= \frac{8}{9} y + 1 \\ \\x= \frac{8}{9} (432) + 1 =(8 \times 48)+1 \\ \\x= 384+1 \\ \\ x=385[/tex]

Metode Eliminasi

[tex]x= \frac{8}{9} y + 1 ....kedua\ ruas\ dikalikan\ dengan\ 9 \\ \\ 9x=8y+9 \to 9x-8y=9.....(1)\\ \\ y= \frac{8}{7} x-8 ....kedua\ ruas\ dikalikan\ dengan\ 7 \\ \\ 7y=8x-56 \to 8x-7y=56.....(2) \\ \\ 9x-8y=9 .....( \times 7) \to 63x-56y=63\\ 8x-7y=56 ...( \times 8) \to 64x-56y=448\\ ------------------(-) \\ \\ 63x-64x=63-448 \\ -x=-385 \\ x=385 \\ \\ y= \frac{8}{7} x-8 \\ \\ y= \frac{8}{7} (385)-8 \\ \\ y=(8 \times 55)-8 \\ y=440-8 \\ y=432[/tex]

HP = {385 , 432}