Question 146516
{{{5x/12 - y/6 = 3 }}} Start with the first equation.



{{{12(5x/cross(12)-y/cross(6))=12(3)}}} Multiply both sides by the LCD 12



{{{5x - 2y = 36}}} Distribute and multiply



So we now have the system of equations:


{{{system(5x-2y=36,x+2y=0)}}}





Now add the equations together. In order to add 2 equations, group like terms and combine them


{{{(5x+x)+(-2y+2y)=36+0}}}


Combine like terms and simplify




{{{6x+cross(-2y+2y)=36}}} Notice how the y terms cancel out





{{{6x=36}}} Simplify



{{{x=36/6}}} Divide both sides by {{{6}}} to isolate x



{{{x=6}}} Reduce




Now plug this answer into the top equation {{{5x-2y=36}}} to solve for y


{{{5x-2y=36}}} Start with the first equation



{{{5(6)-2y=36}}} Plug in {{{x=6}}}



{{{30-2y=36}}} Multiply



{{{-2y=36-30}}} Subtract {{{30}}} from both sides.



{{{-2y=6}}} Combine like terms on the right side.



{{{y=(6)/(-2)}}} Divide both sides by {{{-2}}} to isolate {{{y}}}.



{{{y=-3}}} Reduce.



So our answer is

{{{x=6}}} and {{{y=-3}}}




which also looks like *[Tex \LARGE \left(6,-3\right)]





Now let's graph the two equations (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>)



From the graph, we can see that the two equations intersect at *[Tex \LARGE \left(6,-3\right)]. This visually verifies our answer.





{{{
drawing(500, 500, -10,10,-10,10,
  graph(500, 500, -10,10,-10,10, (36-5*x)/(-2), (0-1*x)/(2) ),
  blue(circle(6,-3,0.1)),
  blue(circle(6,-3,0.12)),
  blue(circle(6,-3,0.15))
)
}}} graph of {{{5x-2y=36}}} (red) and {{{x+2y=0}}} (green)  and the intersection of the lines (blue circle).