1. Worked Out Answer 1.2 1f from: Maths in Motion – Theo de Haan

2. 3x + y + 2z = 1 2x – 2y + 4z = -2 x + 2z = -1 You want to eliminate one of the variables from two equations. Let’s say, y from the lower two equations. If you succeed, you will end up with two equations and two unknowns (x and z).

3. 3x + y + 2z = 1 2x – 2y + 4z = -2 x + 2z = -1 You have to manipulate the upper equation. Please note that in this equation the coefficient of y equals 1. This significantly simplifies calculation!

4. 3x + y + 2z = 1 2x – 2y + 4z = -2 x + 2z = -1 Add the upper equation two times to the middle one. +2x+2x 3x + y + 2z = 1 8x + 8z = 0 x + 2z = -1 Now, eliminate x from the middle equation. -8x-8x

5. 3x + y + 2z = 1 2x – 2y + 4z = -2 x + 2z = -1 +2x+2x 3x + y + 2z = 1 8x + 8z = 0 x + 2z = -1 -8x-8x 3x + y + 2z = 1 - 8z = 8 x + 2z = -1 Apparently z = -1. Substitute this result into the bottom equation…

6. 3x + y + 2z = 1 - 8z = 8 x + 2z = -1 Apparently z = -1. Substitute this result into the bottom equation… z = -1 3x + y + 2z = 1 - 8z = 8 x - 2 = -1 x = 1 So, x = 1. Substitute both results in the upper equation… 3 + y - 2 = 1 - 8z = 8 x + 2z = -1 So, y = 0. y = 0