Question 555378



Start with the given system of equations:


{{{2x+y=5}}}

{{{3x-y=10}}}





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


{{{2x+y=5}}} Start with the given equation



{{{1y=5-2x}}}  Subtract {{{2 x}}} from both sides



{{{1y=-2x+5}}} Rearrange the equation



{{{y=(-2x+5)/(1)}}} Divide both sides by {{{1}}}



{{{y=(-2/1)x+(5)/(1)}}} Break up the fraction



{{{y=-2x+5}}} Reduce



Now lets graph {{{y=-2x+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, -2x+5) }}} Graph of {{{y=-2x+5}}}




So let's solve for y on the second equation


{{{3x-y=10}}} Start with the given equation



{{{-y=10-3x}}}  Subtract {{{3 x}}} from both sides



{{{-y=-3x+10}}} Rearrange the equation



{{{y=(-3x+10)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=(-3/-1)x+(10)/(-1)}}} Break up the fraction



{{{y=3x-10}}} Reduce




Now lets add the graph of {{{y=3x-10}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, -2x+5,3x-10) }}} Graph of {{{y=-2x+5}}}(red) and {{{y=3x-10}}}(green)


From the graph, we can see that the two lines intersect at the point ({{{3}}},{{{-1}}})