Solve the system by using the addition method

Question

4/x^2-3/y^2=-23 and 5/x^2+1/y^2=14            

Answer 1

I assume you mean to use the elimination method by adding the
equations together to eliminate one variable and solve for the other.
 
4/x² - 3/y² = -23
5/x² + 1/y² = 14
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multiply 2nd equation through by 3 and add equations
 
4/x² - 3/y² = -23
15/x²+3/y² = 42
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19/x² = 19
 
x² = 1
x = 1
 
4/1² - 3/y² = -23
-3/y²  = -27
-3 = -27y²
 
y² = -3/-27 = 1/9
 
y = 1/3
 
x = 1
y = 1/3
 
check:
4/1² - 3/(1/3)² = -23
4 - 3/(1/9) = -23
4 - 27 = -23
-23 = -23
 
5/1² + 1/(1/3)² = 14
5 + 1/(1/9) = 14
5 + 9 = 14
14 = 14
 
Both equations balance.