\left \{ {{5x-3y=-8} \atop {xy=12}} \right. I don't understand the equation, please someone explain me how to resolve.

Question

`\left \{ {{5x-3y=-8} \atop {xy=12}} \right.`

I don't understand the equation, please someone explain me how to resolve.

Answer 1

`\left \{ {{5x-3y=-8} \atop {xy=12}} \right.\\\\<=>\left \{ {{5x=3y-8} \atop {xy=12}} \right.\\\\<=>\left \{ {{5x=3y-8} \atop {5xy=60}} \right.\\\\<=>\left \{ {{5x=3y-8} \atop {(3y-8)y=60}} \right.\\\\<=>\left \{ {{5x=3y-8} \atop {3y^(2)-8y -60=0}} \right.\\\\<=>\left \{ {{5x=3y-8} \atop {3y^(2)-18y+10y-60 =0}} \right.\\\\\\<=>\left \{ {{5x=3y-8} \atop {3y(y-6)+10(y-6)=0}} \right.\\\\<=>\left \{ {{5x=3y-8} \atop {(3y+10)(y-6)=0}} \right.\\\\`

<=> 5x = 3y - 8

3y + 10 = 0 or y - 6 = 0

<=> 5x = 3y - 8

y = -10/3 or y = 6

+) with y = -10/3 => 5x = -10 - 8 <=> 5x = -18 <=> x = -3.6

+) with y = 6 => 5x = 3.6 - 10 = 8 <=> x = 8/5 = 1.6

Explanation: