Solving a system of equations

Question

Solve the system:
{x²+ y²=25
{x²+ (y + 8)²= 41

Answer 1

We can substitute the second equation into the first equation.  From the second equation,

 

x² = 41 - (y + 8)²

 

x² = 41 - (y² + 16y + 64)

 

x² = -y² - 16y - 23

 

 

Then,

 

-y² - 16y - 23y + y² = 25

 

-16y - 23y = 25

 

-39y = 25

 

     y = -25/39

 

 

Next, plug in this value of y into the first equation to solve for x.

 

x² = (-25/39)² - 16(-25/39) - 23

 

 

Simplify, then take the square-root of the result.  You will get two x values.