# Find all solutions of the system of equations.\begin{cases}y +x^{2}=4x

Find all solutions of the system of equations.
$\left\{\begin{array}{l}y+{x}^{2}=4x\\ y+4x=16\end{array}$

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dessinemoie
Step 1
Solutions of the system of equations.
$y+{x}^{2}=4x$... equation (1)
y+4x=16... equation (2)
take equation (1)
$y+{x}^{2}=4x$
$y=4x-{x}^{2}$... equation (3)
substitute equation (3) in the (2) equation
y+4x=16
$\left(4x-{x}^{2}\right)+4x=16$
${x}^{2}-8x+16=0$
${\left(x-4\right)}^{2}=0$
x=4
Step 2
Now put x=4 in equation 2
y+4x=16
y+4(4)=16
y+16=16
y=16-16
y=0
Thus the solution is [4,0]