Question

Please help me and do by substitution. Please show work

Answer 1

$\left\{\begin{array}{ccc}x^2+y-8=0\\x+y-2=0&|+2\end{array}\right\\\left\{\begin{array}{ccc}x^2+y-8=0\\x+y=2&|-x\end{array}\right\\\left\{\begin{array}{ccc}x^2+y-8=0\\y=2-x\end{array}\right\\\\\text{subtitute y=2-x to the first equation}\\\\x^2+2-x-8=0\\\\x^2-x-6=0\\\\x^2+2x-3x-6=0\\\\x(x+2)-3(x+2)=0\\\\(x+2)(x-3)=0\iff x+2=0\ \vee\ x-3=0\\\\x=-2\ \vee\ x=3\\\\\text{for}\ x=-2\to y=2-(-2)=2+2=4\\\text{for}\ x=3\to y=2-3=-1\\\\Answer:\ x=-2,\ y=4\to(-2,\ 4)\ and\ x=3,\ y=-1\to(3,\ -1)$