Conclusion

In this chapter, you have investigated how to solve equations that contain two variables. A central approach in this respect involves substitution. Accordingly, you solve an equation for one of its values, and then substitute the solution back into the equation to solve for the remaining value. Working with substitution provided a starting point for examining systems of equations. Systems of equations can involve any number of different variables. They can also involve any number of equations.

In this chapter, you started out by examining how to work with systems of two equations. You then moved to three. You first used multiplication and addition to approach equations as sets of variables with coefficients. From this you proceeded to examine systems of equations on a different basis. This basis involved matrices. By considering only the coefficient values of systems of equations, you could generate the elements of matrices. In this chapter, you concentrated on working with 2 × 3 and 3 × 4 matrices. While matrices of much larger dimensions exist, working with these has introduced you to the skills that prove most primary in working with systems of equations.