Standards Map

Mathematics > Course Model Algebra I (Traditional Pathway) > Reasoning with Equations and Inequalities
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Mathematics | Course : Model Algebra I (Traditional Pathway)

Domain - Reasoning with Equations and Inequalities

Cluster - Solve systems of equations.

[AI.A-REI.C.7] - 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.

Resources:


  • Linear equation
    Any equation that can be written in the form Ax + By + C = 0 where A and B cannot both be 0. The graph of such an equation is a line.
  • Quadratic equation
    An equation that includes only second degree polynomials. Some examples are y = 3x2 – 5x2 + 1, x2 + 5xy + y2 = 1, and 1.6a2 +5.9a – 3.14 = 0.
  • Variable
    A quantity that can change or that may take on different values. Refers to the letter or symbol representing such a quantity in an expression, equation, inequality, or matrix.

Predecessor Standards:

  • 8.EE.C.8
    Analyze and solve pairs of simultaneous linear equations.
  • 8.EE.C.8.a
    Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
  • 8.EE.C.8.b
    Solve systems of two linear equations in two variables algebraically (using substitution and elimination strategies), and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • AI.A-CED.A.3
    Represent constraints by linear equations or inequalities, and by systems of linear equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.* For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
  • AI.A-REI.B.4.b
    Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the solutions of a quadratic equation results in non-real solutions and write them as a ± bi for real numbers a and b.
  • AI.A-REI.C.6
    Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
  • AI.A-REI.D.10
    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). Show that any point on the graph of an equation in two variables is a solution to the equation.
  • AI.A-REI.D.11
    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 and make tables of values. Include cases where f(x) and/or g(x) are linear and exponential functions.*
  • GEO.G-GPE.A.1
    Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
  • GEO.G-GPE.B.4
    Use coordinates to prove simple geometric theorems algebraically, including the distance formula and its relationship to the Pythagorean Theorem. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).