Simultaneous equations are used to find two unknowns when given two equations. In vectors, simultaneous equations are used to find two constants in two vector equations. This example shows finding the constants m and n given two vector equations relating points P, Q, R, S, and u of a quadrilateral. The values of m and n are found by substituting one vector equation into the other.

1. Form 4 [simultaneous equation vs. vector]We use simultaneous equation when we have two unknown to solve. In vector, usually we use simultaneous equation when we have to find the two constant in the two different vector.

2. Example:Example of simultaneous equation. Subtitude (1) into (2)

3. Substitute into (1)

4. In the diagram, PQRS is a quadrilateral. PR and QS is a diagonal of the quadrilateral intersection at T. point u lies on PS. It is given that , , and .Given that and where m and n are constant, find the value of m and of n.SRTuPQSolution:Example of vector.

5. Given, Substitute (2) into (1),We use substitute method in simultaneous equation.