Select the concept that you want to explore and use the sliders to discover linear systems from both algebraic and geometric (graphical) perspectives, then try the proposed exercises.
Use the app to verify whether [math]x=2,y=3[/math] (that is, the point with coordinates [math]\left(2,3\right)[/math] ) is the solution of the system [math]\left\{\begin{matrix}-x+y=-1\\2x-y=3\end{matrix}\right.[/math].[br]How can you verify algebraically whether the given point is a solution of the system?
Use the ratios of the coefficients to determine whether the system [math]\left\{\begin{matrix}x+3y=4\\2x+6y=3\end{matrix}\right.[/math] is dependent, independent or inconsistent.
Find the value or values of [math]k\in\mathbb{R}[/math] for which the system [math]\left\{\begin{matrix}-(3-2k)x+5y=1\\(k+2)x-2y=4\end{matrix}\right.[/math] is independent.
Write the equations of a dependent linear system and explain how you obtained them.