Trudy is solving the following system of equations:

$\displaystyle{x}={y}\usepackage{cmbright}\Huge\$

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

She begins by substituting y in for x in the second equation, creating $\displaystyle{y}+{y}={1}\usepackage{cmbright}\Huge\$ . Then she combines like terms for $\displaystyle{2}{y}={1}\usepackage{cmbright}\Huge\$ . Dividing both sides by 2, she finds that $\displaystyle{y}=\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ . Substituting this back into the first equation, she finds that $\displaystyle{x}=\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ as well.

Is she using deductive reasoning?