Solve the system of equations: x2 + y2 = 16 and 3x + y = 4.

Question

i am not sure how to solve this at all

Answer 1

x² + y² = 16 and 3x + y = 4

 

This is the intersection of a line (3x+y=4) and a circle (x²+y²=16).  First, solve 3x + y = 4 for y:

 

3x + y = 4

y = -3x + 4. 

 

Now substitute -3x+4 in place of y in the first equation:

 

x² + y² = 16

x² + (-3x+4)² = 16

x² + 9x² - 24x + 16 = 16

10x² - 24x = 0

2x(5x - 12) = 0

 

x = 0 and 12/5 (=2 ²/₅)

 

Now find y for each value of x:

 

y = -3x+4

• y= -3(0)+4 = 4 when x=0
• y= -3(12/5)+4 = -16/5 when x = 12/5

 

The answers are: (x,y) = (0,4) and (12/5,-16/5)