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How many solutions are there for the system shown below? х+у= 25 ху = -5 ОА. 1 ов. 4 ОО ос. з OD D. 2 о

How many solutions are there for the system shown below? х+у= 25 ху = -5 ОА. 1 ов-example-1
User Yegor Razumovsky
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1 Answer

22 votes
22 votes

Answer:

Choice D. 2 solutions

Step-by-step explanation:

Adding the two equations gives


\begin{gathered} x^2+y^2=25 \\ x-y^2=-5 \\ --------- \\ x^2+x=20 \end{gathered}

Therefore, we have the quadratic equations


x^2+x-20=0

which has the solutions ( using quadratic formula)


x=\frac{-1\pm\sqrt[]{1^2-4(1)(-20)}}{2}
x=\frac{-1\pm\sqrt[]{81}}{2}

meaning we have two values of x that satisfy the system of equations.

Therefore, choice D is the correct answer.

User Necronet
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