Solve the system by using the addition method.

Question

(1)

 

x²+y²=16

4x²+9y²=36

 

(2)

 

x²+y²=17

x²-2y²=-31

 

Answer 1

1)

 

Multiply the circle equation by -4.  Keep the second equation.

 

-4x² - 4y² = 64

4x² + 9y² = 36

 

Now add the equations to eliminate the x terms.

 

You get            5y² = 100

 

 

Solve this equation for y.

 

 

2)

 

Multiply the circle equation by -1.  Keep the second equation.

 

-x² - y² = -17

x² - 2y² = -31

 

Add the equations to eliminated the x terms.

 

You get         -3y² = -48

 

 

Solve this equation for y.