Matrix methods: These methods are useful when you want to solve a system efficiently and accurately using mathematical tools. Matrix methods involve using matrices to represent and manipulate systems of linear equations. A matrix is a rectangular array of numbers arranged in rows and columns. A system of linear equations can be written as an augmented matrix, which consists of a matrix with coefficients for each variable and an identity matrix with ones on its main diagonal. Matrix methods can perform operations such as row reduction, Gaussian elimination, Cramer’s rule, or inverse matrices to find the solution. However, matrix methods require some knowledge of algebra and calculus, as well as familiarity with matrices and their properties

Elimination: This method is useful when you want to solve a system by reducing it to a single equation with two variables. Elimination works well when the constants of both equations are already isolated or when the coefficients of the Xs or Ys in both equations are the same. However, elimination can be difficult when one or both whole equations have to be multiplied by a number to make the variable cancel. Elimination also requires that both equations have X or Y isolated, which may not be possible in some case.

Substitution: This method is useful when you want to solve a system by eliminating one variable at a time. However, substitution requires that at least one variable in one of the equations is already isolated, which may not be easy to find. Substitution also poses problems for those who tend to make arithmetic mistakes.

Graphing: This method is useful when you want to visualize the relationship between the variables and check your answer visually. However, graphing can be tedious and time-consuming for large systems or complex equations. Graphing also requires that both equations have Y isolated, which may not be possible in some cases.