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There are two main ways to solve equations, algebraically or by using matrices. There are also different subcategories of each way to solve the equations. Using matrices or solving algebraically has some differences and similarities. There are a few ways to solve equations algebraically. One line of attack is by substitution. In substitution, the goal is to solve for one of the variables in the first equation then substitute that variable into the second equation. …

…I prefer using the linear combination method. Even though it is some writing, I believe it is one of the simpler ways to solve equations. There are two main ways to solve equations, algebraically and using matrices. Some people prefer one method to the other, or they use whichever method to their convenience. The subcategories of algebraically solving equations and using matrices are designed to give choices of how to solve equations using different techniques.