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andreev551 [17]
4 years ago
6

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

Mathematics
1 answer:
zhenek [66]4 years ago
6 0

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

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