Next, let’s check (0,1) in the original two-variable quadratic equation:
2 x^2 −y+ 1 = 0
2 × 02 − 1 + 1 = 0
2 × 0 − 1 + 1 = 0
0 − 1 + 1 = 0
− 1 + 1 = 0
0 = 0
Finally, let’s check (−3/2,11/2) in that same equation:
2 x^2 −y+ 1 = 0
2 × (−3/2)^2 − 11/2 + 1 = 0
2 × 9/4 − 11/2 + 1 = 0
9/2− 11/2 + 1 = 0
−2/2+ 1 = 0
− 1 + 1 = 0
0 = 0
- Here are the two equations in their original forms:
3 x+y− 1 = 0
and
2 x^2 − 3 x−y+ 3 = 0
We can manipulate these to obtain the following functions of x:
y=− 3 x+ 1
and
y= 2 x^2 − 3 x+ 3
When we mix the right sides of these equations, we obtain
− 3 x+ 1 = 2 x^2 − 3 x+ 3
which can be rewritten in standard form as the quadratic equation
2 x^2 + 2 = 0
Chapter 27 701
