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Mathematics > Grade 8 > Expressions and Equations
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Mathematics | Grade : 8

Domain - Expressions and Equations

Cluster - Analyze and solve linear equations and pairs of simultaneous linear equations.

[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.

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.
  • 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:

No Predecessor Standards found.

Successor Standards:

  • AI.A-CED.A.2
    Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
  • 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-CED.A.4
    Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations (Properties of equality).* For example, rearrange Ohm’s law R=V2/P to solve for voltage, V. Manipulate variables in formulas used in financial contexts such as for simple interest, I=Prt.
  • AI.A-REI.C.5
    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.
  • 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.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.
  • 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.12
    Graph the solutions of 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 of a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
  • GEO.G-GPE.B.5
    Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
  • MI.A-CED.A.2
    Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
  • MI.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.
  • MI.A-CED.A.4
    Rearrange formulas to highlight a quantity of interest, using the same reasoning (Properties of equality) as in solving equations.* For example, rearrange Ohm’s law, V = IR, to solve for resistance, R. Manipulate variables in formulas used in financial contexts such as for simple interest, I=Prt .
  • MI.A-REI.C.5
    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.
  • MI.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.
  • MI.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.
  • MI.A-REI.D.12
    Graph the solutions of 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 of a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
  • MI.G-GPE.B.5
    Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
  • MII.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.

Same Level Standards:

No Same Level Standards found.