Let $\displaystyle{x}=\usepackage{cmbright}\Huge\$ the smallest, $\displaystyle{y}=\usepackage{cmbright}\Huge\$ the middle, and $\displaystyle{z}=\usepackage{cmbright}\Huge\$ the largest number. The system is

$\displaystyle{x}+{y}+{z}={19}\usepackage{cmbright}\Huge\$ , $\displaystyle{y}={2}{x}\usepackage{cmbright}\Huge\$ , and $\displaystyle{4}{x}-{z}={2}\usepackage{cmbright}\Huge\$

Substitute the second equation into the first: $\displaystyle{x}+{2}{x}+{z}={19}\usepackage{cmbright}\Huge\$ or $\displaystyle{3}{x}+{z}={19}\usepackage{cmbright}\Huge\$

Add this to the third equation: $\displaystyle{7}{x}={21}\usepackage{cmbright}\Huge\$ or $\displaystyle{x}={3}\usepackage{cmbright}\Huge\$

Substitute into the previous equation to get $\displaystyle{9}+{z}={19}\usepackage{cmbright}\Huge\$ , so $\displaystyle{z}={10}\usepackage{cmbright}\Huge\$

Substitute into the second equation to get $\displaystyle{y}={6}\usepackage{cmbright}\Huge\$ .