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Solve the following system. (Use (x,y) format in a single answer space.)

x2 + y2 = 25
y2 - x2 = 7
The solution set is

2 Answers

5 votes

Answer:

(3;4); (-3;-4); (3;-4); (-3;4)

Explanation:

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Solve the following system. (Use (x,y) format in a single answer space.) x2 + y2 = 25 y-example-1
User Janel
by
8.2k points
3 votes

Answer: The required solution set is

(x, y) = (3, 4), (-3, 4), (3, -4) and (-3, -4).

Step-by-step explanation: We are given to solve the following system :


x^2+y^2=25~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y^2-x^2=7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

We will be using the method of Elimination to solve the problem.

Adding equations (i) and (ii), we have


(x^2+y^2)+(y^2-x^2)=25+7\\\\\Rightarrow 2y^2=32\\\\\Rightarrow y^2=16\\\\\Rightarrow y=\pm√(16)~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow y=\pm4.

From equation (ii), we get


(\pm4)^2-x^2=7\\\\\Rightarrow 16-x^2=7\\\\\Rightarrow x^2=16-7\\\\\Rightarrow x^2=9\\\\\Rightarrow x=\pm\sqrt9~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm3.

Thus, the required solution set is

(x, y) = (3, 4), (-3, 4), (3, -4) and (-3, -4).

User ThisIsSparta
by
8.3k points

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