## Simultaneous Equations

Simultaneous equations involve at least two unknown that must be found. If we have two equations and two unknowns or three equations and three unknowns then we can generally solve the equations. Typically the two unknowns are labelled and as in the following simultaneous equations. (1) (2)

The procedure for solving simultaneous equations is:

1. Choose or and make the size of the coefficients of or the same. In the above equations the coefficients of are 2 and 3, and the coefficients of are 1 and 2. We can make the coefficients of the same by multiplying (1) by 2, then both equations have The new equations are (3) (2)

1. We can now eliminate the terms by subtracting: gives 2. Now find by substituting this value for back into one of the equations (1) or (2) and solve to find Suppose we substitute into Example: Solve the simultaneous equations (4) (5)

We can make the coefficients the same size by multiplying (4) by 2 and multiplying (5) by 3. This will result in them being the same size but having opposite sign. We do not subtract – we add to eliminate the - terms. (6) (7)

(6)+(7) gives Substitute into (4) to obtain #### Add comment Refresh