14. Find the solution of the given system of equations, ) x-2y=6 2x-4y=12

To solve the given system of equations, we can use the method of substitution or elimination. In this case, we can use the elimination method.<br /><br />First, let's multiply the first equation by 2 to make the coefficients of x in both equations equal:<br /><br />$\begin{cases} 2x-4y=12\\ 2x-4y=12\end{cases}$<br /><br />Now, we can subtract the second equation from the first equation to eliminate x:<br /><br />$(2x-4y)-(2x-4y)=12-12$<br /><br />$0=0$<br /><br />This result indicates that the two equations are dependent, meaning they represent the same line. Therefore, there are infinitely many solutions to this system of equations.<br /><br />To express the solution set, we can solve for x in terms of y using the first equation:<br /><br />$x-2y=6$<br /><br />$x=2y+6$<br /><br />So, the solution set can be written as:<br /><br />$\{(x,y)\mid x=2y+6, y\in \mathbb{R}\}$<br /><br />This means that for any real number y, we can find a corresponding value of x that satisfies both equations.