1. Unit 25 Solving Equations Presentation 1 Algebraic Fractions Presentation 2 Algebraic Fractions and Quadratic Equations Presentation 3 Solving Simultaneous Equations: One Linear and One Quadratic Presentation 4 Note

2. Unit 25 Solving Equations 25.1 Algebraic Fractions

3. You can sometimes simplify fractions when the numerator and denominator are factorial. Example Simplify ? ? ? ? ? ? ? ? ?

4. Unit 25 Solving Equations 25.2 Algebraic Fractions and Quadratic Equations

5. Solution First combine the two fractions on the LHS by putting them over a common denominator. ? Simplify to give Divide each term by 4 Factorise Either or So or Example Solve ? ? ? ? ? ? ? Multiply both sides byto give ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ?

6. Unit 25 Solving Equations 25.3 Solving Simultaneous Equations: One Linear and One Quadratic

7. To solve simultaneous equations when one is linear and one quadratic, you have to first eliminate one variable. You can do this by substituting one of the variables from the linear equation into the quadratic equation, forming a new quadratic in just one variable. Example Solve the simultaneous equation This is a quadratic that can be factorised to give Solution You can eliminate y by taking one equation from the other to give or ? ? ? ? So or and or ? ? ? Either or etc.

8. Unit 25 Solving Equations 25.4 Note

9. Note The solution, or, are in fact the points of intersection of the line with the quadratic function This is shown in the graph below