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 Solve the system, using any method.  y = x + 2 and x + 2y = 25

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Everest2017idn
Y = X + 2          X + 2 Y = 25

Iin the 2nd equation,  let us Substitute in place of Y its value : X + 2

We get     X + 2 (X + 2) = 25

X + 2 X + 4 = 25
3 X + 4 = 25
3 X = 25 -4 = 21

X = 7

Now use the 1st equation:  Y = X + 2 = 7 + 2 = 9
[tex]Elimination\ method\\\\\left\{\begin{array}{ccc}y=x+2&|subtract\ "x"\ from\ both\ sides\\x+2y=25\end{array}\right\\+\left\{\begin{array}{ccc}-x+y=2\\x+2y=25\end{array}\right|add\ the\ equations\ sides\ \\\----------\\.\ \ \ \ \ \ \ 3y=27\ \ \ \ \ |divide\ both\ sides\ by\ 3\\.\ \ \ \ \ \ \ \ \ \ y=9\\\\subtitute\ y=9\ to\ second\ equation\\x+2(9)=25\\x+18=25\ \ \ \ \ \ \ |subtract\ 18\ from\ both\ sides\\x=7\\\\Solution:x=7\ and\ y=9\to(7;\ 9)[/tex]
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