Reasoning with Equations and Inequalities

A1.AREI.1Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original.A1.AREI.10Explain that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.A1.AREI.11Solve an equation of the form f(x)=g(x) graphically by identifying the x-coordinate(s) of the point(s) of intersection of the graphs of y=f(x) and y=g(x). (Limit to linear; quadratic; exponential.)A1.AREI.12Graph the solutions to a linear inequality in two variables.A1.AREI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.A1.AREI.4Solve mathematical and real-world problems involving quadratic equations in one variable. (Note: A1.AREI.4a and 4b are not Graduation Standards.)A1.AREI.4aUse the method of completing the square to transform any quadratic equation in x into an equation of the form (x-h)^2=k that has the same solutions. Derive the quadratic formula from this form.A1.AREI.4bSolve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a+bi for real numbers a and b. (Limit to non-complex roots.)A1.AREI.5Justify that the solution to a system of linear equations is not changed when one of the equations is replaced by a linear combination of the other equation.A1.AREI.6Solve systems of linear equations algebraically and graphically focusing on pairs of linear equations in two variables. (Note: A1.AREI.6a and 6b are not Graduation Standards.)A1.AREI.6aSolve systems of linear equations using the substitution method.A1.AREI.6bSolve systems of linear equations using linear combination.
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