Question 180245



Start with the given system of equations:


{{{system(6x-y=-35,5x-2y=-35)}}}




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 first equation


{{{6x-y=-35}}} Start with the first equation



{{{-y=-35-6x}}}  Subtract {{{6x}}} from both sides



{{{-y=-6x-35}}} Rearrange the equation



{{{y=(-6x-35)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=((-6)/(-1))x+(-35)/(-1)}}} Break up the fraction



{{{y=6x+35}}} Reduce




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


Since {{{y=6x+35}}}, we can now replace each {{{y}}} in the second equation with {{{6x+35}}} to solve for {{{x}}}




{{{5x-2highlight((6x+35))=-35}}} Plug in {{{y=6x+35}}} into the second equation. In other words, replace each {{{y}}} with {{{6x+35}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{5x+(-2)(6)x+(-2)(35)=-35}}} Distribute {{{-2}}} to {{{6x+35}}}



{{{5x-12x-70=-35}}} Multiply



{{{-7x-70=-35}}} Combine like terms on the left side



{{{-7x=-35+70}}}Add 70 to both sides



{{{-7x=35}}} Combine like terms on the right side



{{{x=(35)/(-7)}}} Divide both sides by -7 to isolate x




{{{x=-5}}} Divide






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



So the first part of our answer is: {{{x=-5}}}










Since we know that {{{x=-5}}} we can plug it into the equation {{{y=6x+35}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=6x+35}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=6(-5)+35}}} Plug in {{{x=-5}}}



{{{y=-30+35}}} Multiply



{{{y=5}}} Combine like terms 




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



So the second part of our answer is: {{{y=5}}}










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


So our answers are:


{{{x=-5}}} and {{{y=5}}}


which form the point *[Tex \LARGE \left(-5,5\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(-5,5\right)]. This visually verifies our answer.





{{{
drawing(500, 500, -10,10,-10,10,
  graph(500, 500, -10,10,-10,10, (-35-6*x)/(-1), (-35-5*x)/(-2) ),
  blue(circle(-5,5,0.1)),
  blue(circle(-5,5,0.12)),
  blue(circle(-5,5,0.15))
)
}}} graph of {{{6x-y=-35}}} (red) and {{{5x-2y=-35}}} (green)  and the intersection of the lines (blue circle).