Since the solution of the system must be a solution to both of the equations in the system, check the point in each equation. Substitute 1 for x and $\displaystyle-{3}\usepackage{cmbright}\Huge\$ for y.

$\displaystyle-{3}={3}{\left({1}\right)}-{6}\usepackage{cmbright}\Huge\$ $\displaystyle{4}{\left({1}\right)}-{2}{\left(-{3}\right)}={10}\usepackage{cmbright}\Huge\$

$\displaystyle-{3}={3}-{6}\usepackage{cmbright}\Huge\$ $\displaystyle{4}+{6}={10}\usepackage{cmbright}\Huge\$

$\displaystyle-{3}=-{3}\usepackage{cmbright}\Huge\$ $\displaystyle{10}={10}\usepackage{cmbright}\Huge\$

Since both equations are true, $\displaystyle{\left({1},-{3}\right)}\usepackage{cmbright}\Huge\$ is a solution to the system.

$\displaystyle-{3}={3}{\left({1}\right)}-{6}\usepackage{cmbright}\Huge\$	$\displaystyle{4}{\left({1}\right)}-{2}{\left(-{3}\right)}={10}\usepackage{cmbright}\Huge\$
$\displaystyle-{3}={3}-{6}\usepackage{cmbright}\Huge\$	$\displaystyle{4}+{6}={10}\usepackage{cmbright}\Huge\$
$\displaystyle-{3}=-{3}\usepackage{cmbright}\Huge\$	$\displaystyle{10}={10}\usepackage{cmbright}\Huge\$