1. in two or more complete sentences, explain how to solve the system of equations algebraically.

2. solve the system of equations. in your final answer, include all of your work.

  best answer:     x + y = 2 
y = -1/4 x² + 3 
we will solve this using substitution method. 
first of all, let us find the value of x in the first equation. 
x + y = 2 
move y to the other side. 
x = 2 - y 
substitute that value of x in the quadratic equation. 
y = -1/4 x² + 3 
y = -1/4(2 - y)² + 3 
expand. 
y = -1/4(4 - 4y + y²) + 3 
distribute the -1/4 to each of the terms in the brackets. 
y = -1 + y - 1/4 y² + 3 
move everything to the left hand side. 
1/4 y² - 2 = 0 
take out 1/4 as a common factor. 
1/4(y² - 8) = 0 
solve the quadratic equation. 
1/4(y² = 8) 
square root both sides. 
1/4(y = ± √8) 
we found the values of y. now we need to find the values of x using one of the original equations. we know that x = 2 - y. all you need to do now is to substitute the values of y into the equation. 
x = 2 - √8 or x = 2 - -√8 
x = 2 - √8 or x = 2 + √8 
final answer:  
(x1, y1) = (2 - √8, √8) 
(x2, y2) = (2 + √8, -√8) 

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