Question 145840



Start with the given system of equations:


{{{x+y=6}}}

{{{x+y=-4}}}





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=6}}} Start with the given equation



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



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





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


{{{x+y=-4}}} Start with the given equation



{{{y=-4-x}}}  Subtract {{{ x}}} from both sides



{{{y=-x-4}}} Rearrange the equation


Now lets add the graph of {{{y=-x-4}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, -x+6,-x-4) }}} Graph of {{{y=-x+6}}}(red) and {{{y=-x-4}}}(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.