IGCSE/GCSE Mathematics - Equations and Inequalities

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

1. 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.
2. Eliminate x or y by - or + everything in the 2 equations.
3. Solve to find one value.
4. Substitute x or y into the equation to find the other value.

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

• E.g. x² - 49

1. Move to one side
2. Factorise
3. Locate B and S (Biggest and Smallest)
4. 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

• 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!

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Drafted by Bonnie (Mathematics)