Question

X 2 + y 2 = 36
x + y = 6

Solve the system of equations.

Answer 1

x = 6 and y = 0 or x = 0 and y = 6 → (6, 0) or (0, 6)

Explanation:

`\left\{\begin{array}{ccc}x^2+y^2=36\\x+y=6&\text{subtract y from both sides}\end{array}\right\\\left\{\begin{array}{ccc}x^2+y^2=36&(1)\\x=6-y&(2)\end{array}\right\qquad\text{substitute (2) to (1):}\\\\(6-y)^2+y^2=36\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\6^2-(2)(6)(y)+y^2+y^2=36\\36-12y+2y^2=36\qquad\text{subtract 36 from both sides}\\2y^2-12y=0\qquad\text{distributive}\\2y(y-6)=0\iff2y=0\ \vee\ y-6=0\\\\2y=0\qquad\text{divide both sides by 2}\\y=0\\\\y-6=0\qquad\text{add 6 to both sides}\\y=6`

`\text{put the values of y to (2):}\\\\for\ y=0:\\x=6-0=6\\\\for\ y=6\\x=6-6=0`