Answer to Question #343002 in Algebra for dodo

Question

Solve this system of equations and provide a graphical representation of the solution. (12)

x2 + y2 = 5

x + y = 1

Answer 1

$\begin{cases} x^2+y^2=5 \\ x+y=1 \end{cases}$

$\begin{cases} x^2+y^2=5 \\ y=1-x \end{cases}$

$x^2+(1-x)^2=5$

$x^2+1-2x+x^2=5$

$2x^2-2x-4=0$

$x^2-x-2=0$

$D=b^2-4ac=1+ 8=9$

$x_1=\frac{1+3}2=2$

$x_2=\frac{1-3}2=-1$

$y_1=-1$

$y_2=2$