Question 124718


Start with the given system of equations:


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

{{{1x+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


{{{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


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



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



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



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



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



{{{y=-x-1}}} Reduce




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


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


From the graph, we can see that the two lines intersect at the point ({{{2}}},{{{-3}}}) (note: you might have to adjust the window to see the intersection)