Question 143376


Start with the given system of equations:


{{{1x+y=6}}}

{{{1x-y=3}}}





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+y=6}}} Start with the given equation



{{{1y=6-x}}}  Subtract {{{ x}}} from both sides



{{{1y=-x+6}}} Rearrange the equation



{{{y=(-x+6)/(1)}}} Divide both sides by {{{1}}}



{{{y=(-1/1)x+(6)/(1)}}} Break up the fraction



{{{y=-x+6}}} Reduce



Now lets graph {{{y=-x+6}}} (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, -x+6) }}} Graph of {{{y=-x+6}}}




So let's solve for y on the second equation


{{{1x-y=3}}} Start with the given equation



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



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



{{{y=(-x+3)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=(-1/-1)x+(3)/(-1)}}} Break up the fraction



{{{y=x-3}}} Reduce




Now lets add the graph of {{{y=x-3}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, -x+6,x-3) }}} Graph of {{{y=-x+6}}}(red) and {{{y=x-3}}}(green)


From the graph, we can see that the two lines intersect at the point ({{{9/2}}},{{{3/2}}}) (note: using a graphing calculator will help you find the point of intersection)