# Common Core: Reasoning with Equations & Inequalities

##### HSA.REI.C9

(+) 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 x 3 or greater).

October 1, 2018
##### HSA.REI.C5

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.

October 1, 2018
##### HSA.REI.C6

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

October 1, 2018
##### HSA.REI.C7

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2 + y2 = 3.

October 1, 2018
##### HSA.REI.C8

(+) Represent a system of linear equations as a single matrix equation in a vector variable.

October 1, 2018
##### HSA.REI.D10

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).

October 1, 2018
##### HSA.REI.D11

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) … Read More “HSA.REI.D11”

October 1, 2018
##### HSA.REI.D12

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

October 1, 2018
##### HSA.REI.A1

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

October 1, 2018
##### HSA.REI.A2

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

October 1, 2018
##### HSA.REI.B3

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

October 1, 2018
##### HSA.REI.B4

Solve quadratic equations in one variable.

October 1, 2018