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

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