$a)$ $Có$ $5x$ $=$ $7y$ $hay$ $\frac{x}{\frac{1}{5}}$ = $\frac{y}{\frac{1}{7}}$ $và$ $y$ $-$$ x$ $=$ $18$
$Áp$ $dụng$ $tính$ $chất$ $của$ $dãy$ $tỉ$ $số$ $bằng$ $nhau:$
$\frac{x}{\frac{1}{5}}$ = $\frac{y}{\frac{1}{7}}$ $=$ $\frac{y - x}{\frac{1}{7} - \frac{1}{5}}$ $=$ $\frac{18}{\frac{-2}{35}}$ $=$ $-315$
$=>$ x = $\frac{1}{5}$ . (-315) = (-63); y = $\frac{1}{7}$ . (-315) = $(-45)$
$Vậy$ $x$ $=$ $-63;$ $y$ $=$ $-45$
$c)$ $Áp$ $dụng$ $tính$ $chất$ $của$ $dãy$ $tỉ$ $số$ $bằng$ $nhau:$
$\frac{x}{2}$ $=$ $\frac{y}{3}$ $=$ $\frac{z}{4}$ $=$ $\frac{x+2y-3z}{2+2.3-3.4}$ $=$ $\frac{-20}{-4}$ $=$ $5$
$=>$ $x$ $=$ $2.5$ $=$ $10$; $y$ = $3.5$ $=$ $15$; $z$ = $4.5$ $=$ $20$.
$Vậy$ $x$ $=$ $10;$ $y$ $=$ $15$; $z$ $=$ $20$
$e)$ $\frac{x-1}{2}$ $=$ $\frac{y-2}{3}$ $=$ $\frac{z-3}{4}$
$=$ $\frac{(x - 1) + 2(y - 2) + 3(z - 3)}{2 +2.3 + 3.4}$
$=$ $\frac{x - 1 + 2y - 4 + 3z - 9}{20}$
$=$ $\frac{(x + 2y + 3z - 9) + (-1-4-9)}{20}$
$=$ $\frac{14-14}{20}$
$=$ $0$
$=>$ $\frac{x-1}{2}$ $=$ $0$ $=>$ $x-1$ $=$ $0$ $=>$ $x$ $=$ $0$ $+$ $1$ $=$ $1$
$=>$ $\frac{y-2}{3}$ $=$ $0$ $=>$ $y-2$ $=$ $0$ $=>$ $y$ $=$ $0$ $+$ $2$ $=$ $2$
$=>$ $\frac{z-3}{4}$ $=$ $0$ $=>$ $z-3$ $=$ $0$ $=>$ $z$ $=$ $0$ $+$ $3$ $=$ $3$
$Vậy$ $x$ $=$ $1;$ $y$ $=$ $2;$ $z$ $=$ $3.$
