Incorrect. The correct system is

$\displaystyle{x}+{y}+{z}={1},{600}\usepackage{cmbright}\Huge\$

$\displaystyle{5}{x}={z}\usepackage{cmbright}\Huge\$ or $\displaystyle{5}{x}-{z}={0}\usepackage{cmbright}\Huge\$

$\displaystyle{0.02}{x}+{0.04}{y}+{0.07}{z}={90}\usepackage{cmbright}\Huge\$

Multiply by 100 to get rid of decimals: $\displaystyle{2}{x}+{4}{y}+{7}{z}={9},{000}\usepackage{cmbright}\Huge\$

Multiply the first equation by $\displaystyle-{4}\usepackage{cmbright}\Huge\$ and add it to the third new equation to eliminate y. Together with the second equation, you now have a system of two equations and two variables to solve.