Question 146196



Start with the given system of equations:


{{{system(9x+5y=-8,-5x+y=12)}}}




Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.





So let's isolate y in the second equation


{{{-5x+y=12}}} Start with the second equation



{{{y=12+5x}}} Add {{{5x}}} to both sides



{{{y=5x+12}}} Rearrange the equation





---------------------


Since {{{y=5x+12}}}, we can now replace each {{{y}}} in the first equation with {{{5x+12}}} to solve for {{{x}}}




{{{9x+5highlight((5x+12))=-8}}} Plug in {{{y=5x+12}}} into the first equation. In other words, replace each {{{y}}} with {{{5x+12}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{9x+(5)(5)x+(5)(12)=-8}}} Distribute {{{5}}} to {{{5x+12}}}



{{{9x+25x+60=-8}}} Multiply



{{{34x+60=-8}}} Combine like terms on the left side



{{{34x=-8-60}}}Subtract 60 from both sides



{{{34x=-68}}} Combine like terms on the right side



{{{x=(-68)/(34)}}} Divide both sides by 34 to isolate x




{{{x=-2}}} Divide






-----------------First Answer------------------------------



So the first part of our answer is: {{{x=-2}}}










Since we know that {{{x=-2}}} we can plug it into the equation {{{y=5x+12}}} (remember we previously solved for {{{y}}} in the second equation).




{{{y=5x+12}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=5(-2)+12}}} Plug in {{{x=-2}}}



{{{y=-10+12}}} Multiply



{{{y=2}}} Combine like terms 




-----------------Second Answer------------------------------



So the second part of our answer is: {{{y=2}}}










-----------------Summary------------------------------


So our answers are:


{{{x=-2}}} and {{{y=2}}}


which form the point *[Tex \LARGE \left(-2,2\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(-2,2\right)]. This visually verifies our answer.





{{{
drawing(500, 500, -10,10,-10,10,
  graph(500, 500, -10,10,-10,10, (-8-9*x)/(5), (12--5*x)/(1) ),
  blue(circle(-2,2,0.1)),
  blue(circle(-2,2,0.12)),
  blue(circle(-2,2,0.15))
)
}}} graph of  {{{9x+5y=-8}}}(red) and  {{{-5x+y=12}}}(green)  and the intersection of the lines (blue circle).