Core 1: Algebraic Skills Part 2

In this section, you learn some new skills, in particular how to solve simultaneous equations.

You will apply these to geometrical situations

1) Linear simultaneous equations

2) Quadratic simultaneous equations

These skills will then be explored in more detail in the chapter on geometry

3) Binomial expansion for positive integer powers

4) Understanding factorials

5) Finding individual coefficients from binomial expansion

6) Harder example, for those wishing to go for the top-grades! (Surely that is all of you...)

Linear simultaneous equations

Solve: (1)-(2) Substitute this value into (2)	Solving simultaneous equations finds where the graphs intersect. We have therefore found that the red and blue line intersect where the x-coordinate is 2.25 and the y-coordinate is 0.5
Create a common coefficient (3) (1)×2 (4) (2)×3 (3)+(4)	See if you can show that:

Quadratic simultaneous equations

So	These graphs intersect in two places, so there should be two possible solutions.
Because	You can see the graphs intersect at (-2. -1) and (-1, 0)

Binomial expansion