Harga 2 kg gula pasir dan 5 kg beras adalah Rp 78.000,-, sedangkan harga 6 kg gula pasir dan 7 kg beras adalah Rp 154.000,-. a. Tentukan harga 1 kg gula pasir dan 1 kg beras b. Tentukan harga 8 kg gula pasir dan 10 kg beras.

<p>Jawaban yang tepat adalah</p><ul><li>1 kg gula pasir = Rp. 14.000; dan 1 kg beras adalah Rp. 10.000;</li><li>Harga 8 kg gula pasir dan 10 kg beras adalah Rp. 212.000;</li></ul><p>&nbsp;</p><p>Pembahasan :</p><p>Misalkan x = gula pasir dan y = beras maka kalimat matematikanya menjadi :</p><p>2x + 5y = 78.000 &nbsp; &nbsp; &nbsp; &nbsp;(1)</p><p>6x + 7y = 154.000 &nbsp; &nbsp; (2)</p><p>&nbsp;</p><p>a. Eliminasi x untuk mendapatkan nilai y</p><p>2x + 5y = 78.000 &nbsp;--&gt; (dikali 3) --&gt; 6x + 15y = 234.000</p><p>6x + 7y = 154.000 --&gt;(dikali 1)--&gt; <u>6x + 7y = 154.000 &nbsp;&nbsp;</u> _</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;8y = 80.000</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y = 80.000 : 8</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y = 10.000</p><p>Substitusikan y = 10.000 ke persamaan (1)</p><p>2x + 5y = 78.000&nbsp;</p><p>2x + 5(10.000) = 78.000&nbsp;</p><p>2x + 50.000 = 78.000</p><p>2x = 78.000 - 50.000</p><p>2x = 28.000</p><p>x = 28.000: 2</p><p>x = 14.000</p><p>Harga 1 kg Gula pasir adalah Rp. 14.000; dan harga 1 kg beras adalah Rp. 10.000;</p><p>&nbsp;</p><p>b. Mencari harga 8 kg gula pasir dan 10 kg beras</p><p>&nbsp; &nbsp; &nbsp;8x + 10 y = 8(14.000) + 10(10.000)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 112.000 + 100.000</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 212.000;</p><p>&nbsp; &nbsp; Harga 8 kg gula pasir dan 10 kg beras adalah Rp. 212.000;</p>