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When it comes to IGCSE/GCSE Maths, do you remember how to eliminate co-efficient?

**Co-efficient Elimination**

- Look to see which (x or y) has the same coefficient. If they do not have the same co-efficient, multiply/divide the equation accordingly to get the same.
- Eliminate x or y by - or + everything in the 2 equations.
- Solve to find one value.
- Substitute x or y into the equation to find the other value.

**Substitution**

- Re-arrange formula to create a formula for the value (y or x) that has the same co-efficient.
- Substitute this new formula into the equation, replacing y/x.
- Solve to find the other value.
- Substitute into the original equation to find 1st value.

**Inequalities**

- E.g. x² - 49

- Move to one side
- Factorise
- Locate B and S (Biggest and Smallest)
- As > 0 ⟶ x > B, x < S

- x² - 49 > 0

→ (x + 7)(x - 7) > 0

→ B = 7, S = -7

→ x > 7, x < -7

< 0 ⟶ S < x < B (1 equation)

> 0 ⟶ x > B, x < S (2 separate answers)

- When you multiply by a negative number, you must flip the inequality.
- E.g. 3 < 9 x-3

= -9 > -27

**Plotting Inequalities**

- Use cover up method to plot line.
- When using cover up, x and y must be on the same side of the equation.
- One must be replaced with 0 to create a new equation and co-ordinates of (0,y) and (x,0).
- Use random co-ordinates to work out the area to shade, by applying them into the inequality.
- E.g. (2,2) into y ≤ 2x +1

(2,2) — 2 ≤ 4 + 1

That's the end of the topic!

Drafted by Bonnie (Mathematics)