Worked Out Answer 1.2 1f

from: Maths in Motion – Theo de Haan

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).

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!

3x + y + 2z = 1

2x – 2y + 4z = -2

x + 2z = -1

Add the upper equation two times to the middle one.

+2x

3x + y + 2z = 1

8x + 8z = 0

x + 2z = -1

Now, eliminate x from the middle equation.

-8x

3x + y + 2z = 1

2x – 2y + 4z = -2

x + 2z = -1

+2x

3x + y + 2z = 1

8x + 8z = 0

x + 2z = -1 -8x

3x + y + 2z = 1

- 8z = 8

x + 2z = -1

Apparently z = -1. Substitute this result into the bottom equation…

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