Question 144394

Start with the given system of equations:


{{{1x+y=3}}}

{{{1x-y=5}}}





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=3}}} Start with the given equation



{{{1y=3-x}}}  Subtract {{{ x}}} from both sides



{{{1y=-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 graph {{{y=-x+3}}} (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+3) }}} Graph of {{{y=-x+3}}}




So let's solve for y on the second equation


{{{1x-y=5}}} Start with the given equation



{{{-y=5-x}}}  Subtract {{{ x}}} from both sides



{{{-y=-x+5}}} Rearrange the equation



{{{y=(-x+5)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=(-1/-1)x+(5)/(-1)}}} Break up the fraction



{{{y=x-5}}} Reduce




Now lets add the graph of {{{y=x-5}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, -x+3,x-5) }}} Graph of {{{y=-x+3}}}(red) and {{{y=x-5}}}(green)


From the graph, we can see that the two lines intersect at the point ({{{4}}},{{{-1}}})