Question

Solve the following system. (Use (x,y) format in a single answer space.)
x2 + y2 = 25
y2 - x2 = 7
The solution set is

Answer 1

Answer:

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

Step-by-step explanation:

for more information see the attached picture.

Answer 2

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

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

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).