Question 124407



Start with the given system of equations:


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

{{{1x+y=2}}}





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=8}}} Start with the given equation



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



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



{{{y=(-x+8)/(-1)}}} Divide both sides by {{{-1}}}



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



{{{y=x-8}}} Reduce



Now lets graph {{{y=x-8}}} (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-8) }}} Graph of {{{y=x-8}}}




So let's solve for y on the second equation


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



{{{1y=2-x}}}  Subtract {{{ x}}} from both sides



{{{1y=-x+2}}} Rearrange the equation



{{{y=(-x+2)/(1)}}} Divide both sides by {{{1}}}



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



{{{y=-x+2}}} Reduce




Now lets add the graph of {{{y=-x+2}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, x-8,-x+2) }}} Graph of {{{y=x-8}}}(red) and {{{y=-x+2}}}(green)


From the graph, we can see that the two lines intersect at the point ({{{5}}},{{{-3}}}) (note: you might have to adjust the window to see the intersection)