Question 145018


{{{4x+6y=26}}} Start with the first equation



{{{6y=26-4x}}}  Subtract {{{4 x}}} from both sides



{{{6y=-4x+26}}} Rearrange the equation



{{{y=(-4x+26)/(6)}}} Divide both sides by {{{6}}}



{{{y=(-4/6)x+(26)/(6)}}} Break up the fraction



{{{y=(-2/3)x+13/3}}} Reduce




So the equation is now in slope-intercept form ({{{y=mx+b}}}) where the slope is {{{m=-2/3}}} and the y-intercept is {{{b=13/3}}}




----------------------------------------------






{{{-6x-9y=-39}}} Move onto the second equation



{{{-9y=-39+6x}}} Add {{{6 x}}} to both sides



{{{-9y=+6x-39}}} Rearrange the equation



{{{y=(+6x-39)/(-9)}}} Divide both sides by {{{-9}}}



{{{y=(+6/-9)x+(-39)/(-9)}}} Break up the fraction



{{{y=(-2/3)x+13/3}}} Reduce




So the equation is now in slope-intercept form ({{{y=mx+b}}}) where the slope is {{{m=-2/3}}} and the y-intercept is {{{b=13/3}}}




------------------------------


Since the slope and y-intercept for both equations are the same, this means that there are an infinite number of solutions (since one equation lies on top of the other)