Question

${x}^{2} + {y}^{2} = 9 \\ y = x + 3 \\ x1 = ? \\ x2 = ?$
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Answer 1

Answer:

$\large\boxed{x_1=0,\ x_2=-3}$

Step-by-step explanation:

$x^2+y^2=9\qquad(1)\\\\y=x+3\qquad(2)\\\\\text{Put (2) to (1):}\\\\x^2+(x+3)^2=9\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\x^2+x^2+2(x)(3)+3^2=9\\\\2x^2+6x+9=9\qquad\text{subtract 9 from both sides}\\\\2x^2+6x=0\qquad\text{distributive}\\\\2x(x+3)=0\iff2x=0\ \vee\ x+3=0\\\\2x=0\qquad\text{divide both sides by 2}\\\boxed{x=0}\\\\x+3=0\qquad\text{subtract 2 from both sides}\\\boxed{x=-3}$