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

(2,–2)

Explanation:

Answer 2

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`