Question

Решите систему уравнений $\left \{ {{2^{y-1}=4^{0,5x}} \atop {log3(7x+y)=2}} \right.$

Answer 1

{y-1=x
{7x+y=9;7x+y>0

7(y-1)+y=9
7y-7+y=9
8y=16
y=2
x=y-1=2-1=1
otvet ( 1;2)

Answer 2

$\left \{ {{2^{y-1}=4^{0,5x}} \atop {log_3(7x+y)=2}} \right.\; \; \left \{ {{2^{y-1}=2^{2\cdot 0,5x}} \atop {7x+y=3^2\; ,\; (7x+y)>0}} \right. \; \; \left \{ {{y-1=x} \atop {y=9-7x\; ,\; y<7x}}\right. \; \; \left \{ {{y=x+1} \atop {y=9-7x,\; y<7x}} \right.\\\\x+1=9-7x\; \; ,\; \; \; 8x=8\; \; ,\; \; x=1\\\\y=x+1=1+1=2\; \; \; (y<7x\; \; \to \; \; \; 2<7\cdot 1\; \; verno)\\\\Otvet:\; \; (1,2)\; .$