Question

x+y=2 y=-1/4 x^2 +3 In two or more complete sentences, explain how to solve the system of equations algebraically. Solve the system of equations. In your final answer, include all of your work.

Answer 1

x+y = 2.....(1)

y= (-1/4)x²+3...(2)

by (1) : y = -x+2

subsct in (2) : -x +2 =( -1/4)x²+3

-4x+8 = -x² +12

x²-4x - 4 =0

(x² -4x +4) -4 -4 =0

(x-2)² = 8 =(2√2)²

x-2 = 2√2 or x-2 = - 2√2

x= 2+ 2√2 or x= 2- 2√2

if : x= 2+ 2√2 .....y = -( 2+ 2√2 )+2 = - 2√2

if : x= 2- 2√2 .....y = -( 2- 2√2 )+2 = 2√2

two solutione : (2+ 2√2 , - 2√2 ) , (2- 2√2 , 2√2 )

Explanation:

Answer 2

x+y = 2.....(1)

y= (-1/4)x²+3...(2)

by (1) : y = -x+2

subsct in (2) : -x +2 =( -1/4)x²+3

-4x+8 = -x² +12

x²-4x - 4 =0

(x² -4x +4) -4 -4 =0

(x-2)² = 8 =(2√2)²

x-2 = 2√2 or x-2 = - 2√2

x= 2+ 2√2 or x= 2- 2√2

if : x= 2+ 2√2 .....y = -( 2+ 2√2 )+2 = - 2√2

if : x= 2- 2√2 .....y = -( 2- 2√2 )+2 = 2√2

two solutione : (2+ 2√2 , - 2√2 ) , (2- 2√2 , 2√2 )