G Dear ©2009 – Not to be sold/Free to use Stage 5 Year 9 Simultaneous Equations Substitution Press Ctrl-A G Dear ©2009 – Not to be sold/Free to use

The Substitution Method 1. Make one pronumeral the subject 2. Substitute into the other equation. 3. Solve this equation to find the value of one the variables. 4. Substitute the value into either of the original equations to find the other value. 5. Write as a co-ordinate pair.

The Substitution Method y = 2x - 1 & y = -x + 2 Substitute y 2x - 1 = -x + 2 Add x to both sides y = 2x1-1 3x - 1 = 2 Add 1 to both sides y = 1 3x = 3 x = 1 Simultaneous Solution = (1,1) Substitute x=1

The Substitution Method 2x - y + 1 = 0 & 3x – y - 1 = 0 +y +y 2x + 1 = y 3x – (2x + 1) - 1 = 0 Make y the subject y = 2x + 1 3x – 2x - 1 - 1 = 0 y = 2 x 2 + 1 Substitute y x - 2 = 0 +2 +2 y = 5 x = 2 Simultaneous Solution = (2,5) Substitute x