Solve the following systems of equations. x^2+y^2−19x+y+66=0 x−y−3=0

Solve the following systems of equations.
${x}^{2}+{y}^{2}-19x+y+66=0$
x−y−3=0
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saiyansruleA
Step 1
we have the given two equations
${x}^{2}+{y}^{2}-19x+y+66=0$
x−y−3=0
Step 2
${x}^{2}+{y}^{2}-19x+y+66=0$....(1)
x−y−3=0..........................(2)
from eq(2) we get
x-y=3
x=y+3
now put the value of x in eq (1)
${\left(y+3\right)}^{2}+{y}^{2}-19\left(y+3\right)+y+66=0$
${y}^{2}+6y+9+{y}^{2}-19y-57+y+66=0$
$2{y}^{2}-12y+75-57=0$
$2{y}^{2}-12y+18=0$
${y}^{2}-6y+9=0$
${\left(y-3\right)}^{2}=0$
y=3,3
Step 3
now as x=y+3
x=3+3
x=6
The solutions are (3,6) , (3,6)
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