Question 132037



Start with the given system of equations:


{{{1x-7y=10}}}

{{{-6x+4y=-22}}}





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-7y=10}}} Start with the given equation



{{{-7y=10-x}}}  Subtract {{{ x}}} from both sides



{{{-7y=-x+10}}} Rearrange the equation



{{{y=(-x+10)/(-7)}}} Divide both sides by {{{-7}}}



{{{y=(-1/-7)x+(10)/(-7)}}} Break up the fraction



{{{y=(1/7)x-10/7}}} Reduce



Now lets graph {{{y=(1/7)x-10/7}}} (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, (1/7)x-10/7) }}} Graph of {{{y=(1/7)x-10/7}}}




So let's solve for y on the second equation


{{{-6x+4y=-22}}} Start with the given equation



{{{4y=-22+6x}}} Add {{{6 x}}} to both sides



{{{4y=+6x-22}}} Rearrange the equation



{{{y=(+6x-22)/(4)}}} Divide both sides by {{{4}}}



{{{y=(+6/4)x+(-22)/(4)}}} Break up the fraction



{{{y=(3/2)x-11/2}}} Reduce




Now lets add the graph of {{{y=(3/2)x-11/2}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, (1/7)x-10/7,(3/2)x-11/2) }}} Graph of {{{y=(1/7)x-10/7}}}(red) and {{{y=(3/2)x-11/2}}}(green)


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