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Ahat [919]
2 years ago
10

How many real solutions does this system of equations have? x² + y² = 25 and x-3y=15​

Mathematics
1 answer:
olya-2409 [2.1K]2 years ago
3 0

x - 3y = 15 \\ x = 15 + 3y

(15 + 3y) {}^{2}  + y {}^{2}  = 25

225 + 90y + 9y {}^{2}  + y {}^{2}  = 25

10y {}^{2}  + 90y + 200 = 0

y {}^{2}  + 9y + 20 =  0

(y  + 4)(y  + 5) = 0

y = -  4 \:  \:  \:  \:  \:  \: y = -  5

for \: y=  - 4 \\ x = 15 +  3( - 4) = 15 - 12 = 3

for \: y =  - 5 \\ x = 15 + 3( - 5) = 15 - 15 = 0

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