use the elimination method to solve the non linear system of equation

Question

use the elimination method to solve the non linear system of equation. x^2+y^2=52              

               x^2+10y=76

 

Answer 1

x² + y² = 52            eq1

 

x² + 10y = 76          eq2

 

 

We can subtract eq2 from eq1 to eliminate the x² terms.  This is called the elimination method.

 

y² - 10y = -24

 

 

Now we have an equation in terms of y only.  Solve for y from this equation.

 

y² - 10y + 24 = 0

 

(y - 6)(y - 4) = 0

 

y = 6   ,    y = 4

 

 

Next, we substitute these values into eq1 to solve for x.

 

 

x² + 6² = 52                   and                   x² + 4² = 52

 

x² + 36 = 52                   and                   x² + 16 = 52

 

x² = 16                          and                     x² = 36

 

x = -4                                                       x = -6

 

x = 4                             and                      x = 6

 

 

So we have for pairs of solutions.

 

x = -4                                                     x = -6

y = 6                                                      y = 4

 

 

x = 4                                                      x = 6

y = 6                                                      y = 4

 

 

On your own, validate which solution pair(s) satisfy the equations.