Question 145710

Start with the given system of equations:


{{{x+y=5}}}

{{{x-y=1}}}





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


{{{x+y=5}}} Start with the given equation



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



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




Now lets graph {{{y=-x+5}}} (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+5) }}} Graph of {{{y=-x+5}}}




So let's solve for y on the second equation


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



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



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



{{{y=x-1}}} Divide both sides by -1





Now lets add the graph of {{{y=x-1}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, -x+5,x-1) }}} Graph of {{{y=-x+5}}}(red) and {{{y=x-1}}}(green)


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