Reasoning with Equations and Inequalities
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Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
Represent a system of linear equations as a single matrix equation in a vector variable.
Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).