Question 127777



Start with the given system of equations:


{{{1x-2y=8}}}

{{{3x-2y=12}}}





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


{{{1x-2y=8}}} Start with the given equation



{{{-2y=8-x}}}  Subtract {{{ x}}} from both sides



{{{-2y=-x+8}}} Rearrange the equation



{{{y=(-x+8)/(-2)}}} Divide both sides by {{{-2}}}



{{{y=(-1/-2)x+(8)/(-2)}}} Break up the fraction



{{{y=(1/2)x-4}}} Reduce



Now lets graph {{{y=(1/2)x-4}}} (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)



{{{ graph( 600, 600, -10, 10, -10, 10, (1/2)x-4) }}} Graph of {{{y=(1/2)x-4}}}




So let's solve for y on the second equation


{{{3x-2y=12}}} Start with the given equation



{{{-2y=12-3x}}}  Subtract {{{3 x}}} from both sides



{{{-2y=-3x+12}}} Rearrange the equation



{{{y=(-3x+12)/(-2)}}} Divide both sides by {{{-2}}}



{{{y=(-3/-2)x+(12)/(-2)}}} Break up the fraction



{{{y=(3/2)x-6}}} Reduce




Now lets add the graph of {{{y=(3/2)x-6}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, (1/2)x-4,(3/2)x-6) }}} Graph of {{{y=(1/2)x-4}}}(red) and {{{y=(3/2)x-6}}}(green)


From the graph, we can see that the two lines intersect at the point ({{{2}}},{{{-3}}})