Question

Find the solution(s) of the system of equations: x2 + y2 = 8 y = x – 4 options: (–2,–6) (2,–2) and (–2,–6) (2,–2) No solutions

Answer 1

Answer: x=2 y=-2

(2,-2) one solution

Step-by-step explanation:

Solve by substitution

$\begin{bmatrix}x^2+y^2=8\\ y=x-4\end{bmatrix}$

$\mathrm{Subsititute\:}y=x-4$

$\begin{bmatrix}x^2+\left(x-4\right)^2=8\end{bmatrix}$

$2x^2-8x+16=8$

$\mathrm{Isolate}\:x\:\mathrm{for}\:2x^2-8x+16=8:\quad x=2$

$\mathrm{For\:}y=x-4$

$\mathrm{Subsititute\:}x=2$

$y=2-4$        $2-4=-2$

$y=-2$

$The\:solutions\:to\:the\:system\:of\:equations\:are$

$x=2,\:y=-2$