Ответ:
Объяснение:
\left \{ {{3^{x}+2^{x+y}*2^{1}-5=0} \atop {3^{x}*3^{1}-2^{x+y}-1=0}} \right." alt="\left \{ {{3^{x}+2^{x+y+1}-5=0} \atop {3^{x+1}-2^{x+y}-1=0}} \right.<=>\left \{ {{3^{x}+2^{x+y}*2^{1}-5=0} \atop {3^{x}*3^{1}-2^{x+y}-1=0}} \right." align="absmiddle" class="latex-formula">
замена переменной:
a>0, b>0
получим систему уравнений относительно переменных a и b:
\left \{ {{a+2b-5=0} \atop {6a-2b-2=0}} \right. +" alt="\left \{ {{a+2b-5=0} \atop {3a-b-1=0}|*2} \right. <=>\left \{ {{a+2b-5=0} \atop {6a-2b-2=0}} \right. +" align="absmiddle" class="latex-formula">
\left \{ {{a+2b-5=0} \atop {a=1}} \right.<=>\left \{ {{a=1} \atop {b=2}} \right." alt="\left \{ {{a+2b-5=0} \atop {7a=7}} \right. <=>\left \{ {{a+2b-5=0} \atop {a=1}} \right.<=>\left \{ {{a=1} \atop {b=2}} \right." align="absmiddle" class="latex-formula">
обратная замена:
\left \{ {{3^{x}=3^{0}} \atop {2^{x+y}=2^{1}}} \right. <=>\left \{ {{x=0} \atop {x+y=1}} \right. <=>\left \{ {{x=0} \atop {y=1}} \right." alt="\left \{ {{3^{x}=1 } \atop {2^{x+y} =2}} \right. <=>\left \{ {{3^{x}=3^{0}} \atop {2^{x+y}=2^{1}}} \right. <=>\left \{ {{x=0} \atop {x+y=1}} \right. <=>\left \{ {{x=0} \atop {y=1}} \right." align="absmiddle" class="latex-formula">