Question 342712


Start with the given system of equations:


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




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


{{{2x+y=-2}}} Start with the second equation



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



{{{y=-2x-2}}} Rearrange the equation





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


Since {{{y=-2x-2}}}, we can now replace each {{{y}}} in the first equation with {{{-2x-2}}} to solve for {{{x}}}




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




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



{{{x-4x-4=5}}} Multiply



{{{-3x-4=5}}} Combine like terms on the left side



{{{-3x=5+4}}}Add 4 to both sides



{{{-3x=9}}} Combine like terms on the right side



{{{x=(9)/(-3)}}} Divide both sides by -3 to isolate x




{{{x=-3}}} Divide






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



So the first part of our answer is: {{{x=-3}}}










Since we know that {{{x=-3}}} we can plug it into the equation {{{y=-2x-2}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-2x-2}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-2(-3)-2}}} Plug in {{{x=-3}}}



{{{y=6-2}}} Multiply



{{{y=4}}} Combine like terms 




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



So the second part of our answer is: {{{y=4}}}










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


So our answers are:


{{{x=-3}}} and {{{y=4}}}


which form the point *[Tex \LARGE \left(-3,4\right)] 




If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help">jim_thompson5910@hotmail.com</a>


Also, feel free to check out my <a href="http://www.freewebs.com/jimthompson5910/home.html">tutoring website</a>


Jim