LAC 28:CXLII.3507. Reasoning with Equations and Inequalities

A. Solve System of Equations. 1. Represent a system of linear equations as a single matrix equation in a vector variable. 2. Find the inverse of a matrix if it exists and use it to solve systems of linear equations. Use technology for matrices of dimension 3 × 3 or greater. B. Represent and solve equations and inequalities graphically. 1. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve, which could be a line. Include rational, logarithmic, exponential and polynomial functions. 2. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, quadratic, polynomial, rational, piecewise linear, absolute value, logarithmic and exponential functions. Identify domain restrictions and real and non-real solutions algebraically.