MATH 110 Lecture Notes - Lecture 13: Exclusive Or, Analytic Geometry
Document Summary
If you have two different equations with the same two unknowns in each, you can solve for both unknowns. There are three common methods for solving: addition/subtraction, substitution, and graphing. This method is also known as the elimination method. Now inserting 5 for x in the first equation gives the following: By replacing each x with a 5 and each y with a 2 in the original equations, you can see that each equation will be made true. In example and example , a unique answer existed for x and y that made each sentence true at the same time. In some situations you do not get unique answers or you get no answers. You need to be aware of these when you use the addition/subtraction method. Now the yis preceded by a 3 in each equation. The equations can be subtracted, eliminating the yterms. Insert x = 5 in one of the original equations to solve for y.
=0 is of quadric type. We can solve it by letting 
and 
, and factoring. Or we could solve for 
, square each side, and then solve the resulting quadric equation. Solve the following equations using both methods indicated, and show that you get the same final answers.
quadratic type; multiply by LCD
quadratic type; solve for the radical, and square.
