[tex]4x-y=2 \\ 2x+9y=-12 \\ \\ ---- \\ \\ 4x - y = 2 \\ \\ 4x - y + 4 = 2 + y \\ \\ 4x = 2 + y \\ \\ \frac{4x}{4} = \frac{2+y}{4} \\ \\ x = \frac{2+y}{4} \\ \\ 2 \frac{2+y}{4} + 9y = -12 \\ \\ 9y + \frac{y+2}{2} = -12 \\ \\ 2 \times 9y + 2 \frac{y+2}{2} = -2 \times 12 \\ \\ 19y + 2 = -24 \\ \\ 19y + 2 - 2 = -24 - 2 \\ \\ 19y = -26 \\ \\ \frac{19y}{19} = \frac{-26}{19} \\ \\ y = - \frac{26}{19} \\ \\ [/tex]
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[tex]\\ \\ x = \frac{2+y}{4} \\ \\ y = - \frac{26}{19} \\ \\ x = \frac{2- \frac{26}{19} }{4} \\ \\ x = \frac{3}{19} \\ \\[/tex]
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The final result is: x = 3/19 and y = -26/19.
