Solve for \(x\) in \(2y=x+5\).
Solve for \(x\).
\[2y=x+5\]
Subtract \(5\) from both sides.
\[2y-5=x\]
Switch sides.
\[x=2y-5\]
\[x=2y-5\]
Substitute \(x=2y-5\) into \(4{x}^{2}+4xy+{y}^{2}=0\).
Start with the original equation.
\[4{x}^{2}+4xy+{y}^{2}=0\]
Let \(x=2y-5\).
\[4{(2y-5)}^{2}+4(2y-5)y+{y}^{2}=0\]
Simplify.
\[25{y}^{2}-100y+100=0\]
\[25{y}^{2}-100y+100=0\]
Solve for \(y\) in \(25{y}^{2}-100y+100=0\).
Solve for \(y\).
\[25{y}^{2}-100y+100=0\]
Factor out the common term \(25\).
\[25({y}^{2}-4y+4)=0\]
Rewrite \({y}^{2}-4y+4\) in the form \({a}^{2}-2ab+{b}^{2}\), where \(a=y\) and \(b=2\).
\[25({y}^{2}-2(y)(2)+{2}^{2})=0\]
Use Square of Difference: \({(a-b)}^{2}={a}^{2}-2ab+{b}^{2}\).
\[25{(y-2)}^{2}=0\]
Divide both sides by \(25\).
\[{(y-2)}^{2}=0\]
Take the square root of both sides.
\[y-2=0\]
Add \(2\) to both sides.
\[y=2\]
\[y=2\]
Substitute \(y=2\) into \(x=2y-5\).
Start with the original equation.
\[x=2y-5\]
Let \(y=2\).
\[x=2\times 2-5\]
Simplify.
\[x=-1\]
\[x=-1\]
Therefore,
\[\begin{aligned}&x=-1\\&y=2\end{aligned}\]
x=-1;y=2
