# {2x−y=9}{2x+7y=17}

$\left\{\begin{array}{l}2x-y=9\\ 2x+7y=17\end{array}$

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To solve a system of equations, you should use the substitution method or the elimination method. The substitution method should be used if one of the equations has a variable that can be easily solved for. The elimination method should be used if the equations have a variable term with the same or opposite coefficients or if neither equation can be easily solved for a variable.
The first equation can be easily solved for $yy$ but the equations have the same coefficient for the $xx$ terms so the elimination method will be easier to use.
To use the elimination method, subtract the two equations to eliminate the $xx$ terms. Then solve for y:
$2x+7y=17$
$-\left(2x-y=9\right)$
$8y=8$
$y=1$
Now that you the value of y, substitute it into either equation and then solve for x:
$2x-y=9$
$2x-1=9$
$2x=10$
$x=5$
The solution of the system is then $\left(x,y\right)=\left(5,1\right).$

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