Determine if the ordered pair $$ (1,4) $$ is a solution to the system of equations. $$ 7 x+4 y=23 $$ $$ 4 x+2 y=12 $$

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Solve the system of equations $$ 7x+4y=23;4x+2y=12 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}7x+4y=23\4x+2y=12\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=\frac{23-4y}{7}\4x+2y=12\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$4	imes \frac{23-4y}{7}+2y=12$$
- step3: Simplify:
  $$\frac{4\left(23-4yight)}{7}+2y=12$$
- step4: Multiply both sides of the equation by LCD:
  $$\left(\frac{4\left(23-4yight)}{7}+2yight)	imes 7=12	imes 7$$
- step5: Simplify the equation:
  $$92-2y=84$$
- step6: Move the constant to the right side:
  $$-2y=84-92$$
- step7: Subtract the numbers:
  $$-2y=-8$$
- step8: Change the signs:
  $$2y=8$$
- step9: Divide both sides:
  $$\frac{2y}{2}=\frac{8}{2}$$
- step10: Divide the numbers:
  $$y=4$$
- step11: Substitute the value of $$y:$$
  $$x=\frac{23-4	imes 4}{7}$$
- step12: Calculate:
  $$x=1$$
- step13: Calculate:
  $$\left\{ \begin{array}{l}x=1\y=4\end{array}ight.$$
- step14: Check the solution:
  $$\left\{ \begin{array}{l}x=1\y=4\end{array}ight.$$
- step15: Rewrite:
  $$\left(x,yight) = \left(1,4ight)$$
The ordered pair $$ (1,4) $$ is a solution to the system of equations $$ 7x+4y=23 $$ and $$ 4x+2y=12 $$.
$$ (1,4) $$ is a solution to the system of equations.

Determine if the ordered pair is a solution to the system of equations.

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