Solve the following systems of equations. Show all work.

Question

1). 4x² + 8x + 5 - y = 1

    3x² - x + 3 = y + x + 8

2).   y = x² + 1   

     2x² + 3y = 28

3). 4x² – 2y² = 4

    x²  + y² = 10

Answer 1

2)

y = x^2 + 1

2x^2 + 3y^2 = 28

2x^2 + 3(x^2+1) = 28

2x^2 + 3x^2 + 3 = 28

5x^2 = 28-3 = 25

x^2 = 25/5 = 5

x =sqr5

y = x^2 + 1 = 5 + 1 = 6

y= 6

(sqr5,6) is the solution = (x,y)

6 =(sqr5)^2 +1

6 =5 +1

2(sqr5)^2 +3(6) = 28

2(5) + 18 = 28

10 + 18 = 28