Question 407511


Start with the given system of equations:


{{{system(-2x+y=19,2x+4y=26)}}}




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=19}}} Start with the first equation



{{{y=19+2x}}} Add {{{2x}}} to both sides



{{{y=2x+19}}} Rearrange the equation




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


Since {{{y=2x+19}}}, we can now replace each {{{y}}} in the second equation with {{{2x+19}}} to solve for {{{x}}}




{{{2x+4highlight((2x+19))=26}}} Plug in {{{y=2x+19}}} into the second equation. In other words, replace each {{{y}}} with {{{2x+19}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{2x+(4)(2)x+(4)(19)=26}}} Distribute {{{4}}} to {{{2x+19}}}



{{{2x+8x+76=26}}} Multiply



{{{10x+76=26}}} Combine like terms on the left side



{{{10x=26-76}}}Subtract 76 from both sides



{{{10x=-50}}} Combine like terms on the right side



{{{x=(-50)/(10)}}} Divide both sides by 10 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=2x+19}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=2x+19}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=2(-5)+19}}} Plug in {{{x=-5}}}



{{{y=-10+19}}} Multiply



{{{y=9}}} Combine like terms 




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



So the second part of our answer is: {{{y=9}}}










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


So our answers are:


{{{x=-5}}} and {{{y=9}}}


which form the point *[Tex \LARGE \left(-5,9\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(-5,9\right)]. This visually verifies our answer.





{{{
drawing(500, 500, -10,10,-10,10,
  grid(1),
  graph(500, 500, -10,10,-10,10, (19--2*x)/(1), (26-2*x)/(4) ),
  blue(circle(-5,9,0.1)),
  blue(circle(-5,9,0.12)),
  blue(circle(-5,9,0.15))
)
}}} graph of {{{-2x+y=19}}} (red) and {{{2x+4y=26}}} (green)  and the intersection of the lines (blue circle).





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