# {2x−y=9} {2x+7y=17}

Question
Systems of equations
$$\displaystyle{\left\lbrace{2}{x}−{y}={9}\right\rbrace}$$ $$\displaystyle{\left\lbrace{2}{x}+{7}{y}={17}\right\rbrace}$$

2021-02-07
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
-(2x-y=9)
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 (x,y)=(5,1).

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