Dengan metode gabungan (eliminasi dan substitusi) tentukan himpunan penyelesaian! 3x+5 y=4 2x-y=-6

<p>Halo Almira. Kakak bantu jawab ya.</p><p>Jawab: <strong>{(-2, 2)}</strong></p><p>Pembahasan:</p><p>Langkah 1. Mengeliminasi y untuk menentukan nilai x.</p><p>3x+5y = 4 &nbsp; |×1| &nbsp; 3x+5y =4</p><p>&nbsp; &nbsp;2x-y = -6 &nbsp;|×5| 10x-5y = -30</p><p>^{_______________________________ &nbsp; +}</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;}13x = -26</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x = -2</p><p>Langkah 2. Menentukan nilai y dengan metode substitusi.</p><p>Substitusikan x=-2 ke persamaan 2x-y = -6. Diperoleh</p><p>&nbsp; &nbsp; &nbsp;2x-y = -6</p><p>2(-2)-y = -6</p><p>&nbsp; &nbsp; &nbsp;-4-y = -6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;-y = -2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; y = 2</p><p>&nbsp;</p><p><strong><u>Jadi, himpunan penyelesaiannya adalah {(-2, 2)}.</u></strong></p>