Question

3. Решить систему уравнений:

Answer 1

$\displaystyle\bf\\\left \{ {{x+y=2} \atop {3^{6-x} \cdot 4^{y+3} =36}} \right. \\\\\\\left \{ {{x=2-y} \atop {3^{6-2+y} \cdot 4^{y+3} =36}} \right. \\\\\\\left \{ {{x=2-y} \atop {3^{4+y} \cdot 4^{y+3} =36}} \right. \\\\\\\left \{ {{x=2-y} \atop {3^{y} \cdot 3^{4} \cdot 4^{y} \cdot 4^{3} =36}} \right.\\\\\\\left \{ {{x=2-y} \atop {(3\cdot 4)^{y} \cdot 81\cdot 64=36}} \right.\\\\\\\left \{ {{x=2-y} \atop{12^{y} \cdot 5184=36}} \right.$

$\displaystyle\bf\\\left \{ {{x=2-y} \atop {12^{y}=\dfrac{1}{144 }} \right. \\\\\\\left \{ {{x=2-y} \atop {12^{y}=12^{-2} \right. \\\\\\\left \{ {{x=2-(-2)} \atop {y=-2}} \right. \\\\\\\left \{ {{x=4} \atop {y=-2}} \right. \\\\\\Otvet \ : \ (4 \ ; \ -2)$

Answer 2

Ответ: (4;-2).

Объяснение:

$\displaystyle\\\left \{ {{x+y=2} \atop {3^{6-x}*4^{y+3}=36} \right. \ \ \ \ \ \ \left \{ {{x=2-y} \atop {3^{6-(2-y)}*4^{y+3}}=36}} \right.\ \ \ \ \ \ \left \{ {{x=2-y} \atop {3^{4+y}*4^{3+y}=36}} \right. \\\\\\\left \{ {{x=2-y} \atop {3*3^{3+y}*4^{3+y}=36\ |:3}} \right.\ \ \ \ \ \ \left \{ {{x=2-y} \atop {(3*4)^{3+y}=12}} \right.\ \ \ \ \ \ \left \{ {{x=2-y} \atop {12^{3+y}=12^1}} \right.$

$\displaystyle\\\left \{ {{x=2-y} \atop {3+y=1}} \right. \ \ \ \ \ \ \left \{ {{x=2-(-2)} \atop {y=-2}} \right. \ \ \ \ \ \ \left \{ {{x=4} \atop {y=-2}} \right..$