# Further Maths - Solving Systems of Equations Using Triangle Method

Other than matricies, how can you solve a system of three equations?

Using the triangle method.

How does the triangle method of solving a system of three equations work?

Using back substitution.

What are the steps involved in the triangle method?

- Add/subtract two equations of three variables to form an equation of two variables
- Do this for another equation, forming an equation with the same two variables
- Solve this using simulataneous equations
- Substitute the new values and solve for the final variable

Why is it called the “triangle” method of solving equations?

You work your way from 3 to 1 variables, so it kind of looks like an upside-down pyramid.

If you have the three equations

\[2x-6y+4z = 32 \\ 3x + 2y -9z = -49 \\ -2x + 4y + z = -3\]
, what two equations could you initially pair?

Add equation 1 and equation 3 together.

\[2x - 6y + 4z = 32 -2x + 4y + z = -3\]