Question 126455
First, convert both of the equations to slope-intercept form {{{y=mx+b}}}
M being the slope and b being the y intercept (0,b)

First equation.
{{{x-2y=4}}}

Add 2y to both sides.
{{{x-2y+27=4+2y}}}={{{x=2y+4}}}

Next subtract 4 from each side.
{{{x-4=2y+4-4}}}={{{x-4=2y}}}

Now divide each side by 2 to isolate the y variable.
{{{x/2-4/2=2y/2}}}={{{(1/2)x-2=y}}}

Now repeat the process for the second equation.

{{{x+2y=12}}}

Subtract x from both sides
{{{x-x+2y=12-x}}}={{{2y=-x+12}}}

Now divide both sides by 2 to isolate the y variable
{{{2y/2=-x/2+12/2}}}={{{y=(-1/2)x+6}}}

Now that both equations are in Slope-intercept form, graph the y intercept of each and use the slope to graph a second point.  Compare the graphs of the two equations.  Note that they intersect at one point only.  This means that the 2 equations have one unique solution and are classified as independent.





{{{graph(300, 300, -20, 20, -20, 20, y=(-1/2)x+6, (1/2)x-2=y )}}}