Saved Bookmarks
| 1. |
(x² + y² -z2)2 - (2xy)2 |
|
Answer» quation 1 x²+y²=2 Equation 2 Find: xy Solution: The approach to a system of 2 equations with two UNKNOWNS is to ascertain if they are independent, and then use either substitution or elimination. As to independence, Equation 1 can be rewritten in Slope-Intercept form as y = -x + 2. So this is a negative SLOPING line, m= -1, passing through point (0, 2). The CIRCLE is centered at the origin and has a radius of sqrt(2). At a 45-degree angle, this circle should pass through the point (1, 1) which is on the line so we’re pretty sure this is a solution. Let’s do the substitution as a check. Step 1 Substitute the VALUE of y from Equation 1 into Equation 2 and solve for x. x²+y²=2 x²+(-x + 2)²=2 x²+x²-4x+4=2 x²-2x+2=1 x²-2x+1=0 (x-1)(x-1)=0 x-1=0 x=1 Substitute x = 1 into either equation and solve for y. y = -x + 2 y = -(1) + 2 y = 1 Answer: xy = 1(1) = 1 |
|