How do you solve the system by graphing #x + 2y = 4 # and #2x + 4y = 8 #?
The simplest method to use might be to rewrite each equation in the slope/intercept form, y = mx + b where m is the slope and b is the y-intercept. Then graph them and see where/if they intercept.
x +2y = 4
y = -1/2x + 2 the slope is -1/2 and the y-intercept is 2.
2x + 4y = 8
4y = -2x + 8
y = -2/4 x +2
y= -1/2 x +2 the slope for this equation is also -1/2 and the
y-intercept is also 2.
If we try to graph these "two" line we quickly see that they are, in fact, the same line, where there is not one point of interception, but rather, all points are common to both.
When graphing the solution to a system of first degree equations like these, there are three possible outcomes. They will intercept at one point (x,y); or, as in this case, they are the same equation and all points are common; or the lines are parallel, they have the same slope but a different y-intercept, and they have no point of interception.