Question 325103



Start with the given system of equations:


{{{system(4x+y=11,x+2y=8)}}}




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


{{{4x+y=11}}} Start with the first equation



{{{y=11-4x}}}  Subtract {{{4x}}} from both sides



{{{y=-4x+11}}} Rearrange the equation


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


Since {{{y=-4x+11}}}, we can now replace each {{{y}}} in the second equation with {{{-4x+11}}} to solve for {{{x}}}




{{{x+2highlight((-4x+11))=8}}} Plug in {{{y=-4x+11}}} into the second equation. In other words, replace each {{{y}}} with {{{-4x+11}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{x+(2)(-4)x+(2)(11)=8}}} Distribute {{{2}}} to {{{-4x+11}}}



{{{x-8x+22=8}}} Multiply



{{{-7x+22=8}}} Combine like terms on the left side



{{{-7x=8-22}}}Subtract 22 from both sides



{{{-7x=-14}}} Combine like terms on the right side



{{{x=(-14)/(-7)}}} Divide both sides by -7 to isolate x




{{{x=2}}} Divide



Since we know that {{{x=2}}} we can plug it into the equation {{{y=-4x+11}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-4x+11}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-4(2)+11}}} Plug in {{{x=2}}}



{{{y=-8+11}}} Multiply



{{{y=3}}} Combine like terms 



So the solutions are {{{x=2}}} and {{{y=3}}}



which form the ordered pair *[Tex \LARGE \left(2,3\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(2,3\right)]. This visually verifies our answer.





{{{
drawing(500, 500, -10,10,-10,10,
  graph(500, 500, -10,10,-10,10, (11-4*x)/(1), (8-1*x)/(2) ),
  blue(circle(2,3,0.1)),
  blue(circle(2,3,0.12)),
  blue(circle(2,3,0.15))
)
}}} graph of {{{4x+y=11}}} (red) and {{{x+2y=8}}} (green)  and the intersection of the lines (blue circle).







So you have the correct answers (you probably want to say x=2 and y=3)