Multiply the first equation by $\displaystyle-{4}\usepackage{cmbright}\Huge\$ : $\displaystyle-{8}{x}-{4}{y}=-{76}\usepackage{cmbright}\Huge\$

Add this to $\displaystyle{3}{x}+{4}{y}={1}\usepackage{cmbright}\Huge\$ to get: $\displaystyle-{5}{x}=-{75}\usepackage{cmbright}\Huge\$

Solve for x to get $\displaystyle{x}={15}\usepackage{cmbright}\Huge\$ , and substitute this into the first equation:

$\displaystyle{2}{\left({15}\right)}+{y}={19}\usepackage{cmbright}\Huge\$ or $\displaystyle{30}+{y}={19}\usepackage{cmbright}\Huge\$ , so $\displaystyle{y}=-{11}\usepackage{cmbright}\Huge\$