Big Idea:

Big Idea 2

A solution simultaneously makes each function rule in a system of equations (or inequalities) true.

1 week

Evidence of Understanding

  • construct equations within a system that maintain the system’s solution set
    • analyze terms in the equations of a system to strategically rewrite them in 1 variable
      • recognize equivalent terms shared by both equations in a system and use substitution to rewrite one variable in terms of another
      • create equivalent terms in both functions by multiplying by a strategic quantity
    • identify the lowest common multiple for common terms in a system and use it to construct equations or inequalities in the system that will produce the same solution set 
      • Example: for 2x + 3y = 7 and 3x - 5y = 8, recognize that 6x is the lowest common multiple of 2x and 3x and create 6x + 9y = 21 and 6x - 10y = 16 that will have the same solution set
    • prove that adding one equation to a multiple of the other equation in the system produces a system with the same solution set
      • create diagrams or visual models to show that the solution sets are equivalent
    • recognize and justify when systems of equations will have the same solution set


  • solve a system of equations using substitution or elimination
    • estimate and justify reasonable and unreasonable solution options
    • describe the quantitative features of a system and justify whether substitution or elimination is a better solution method
    • determine the solution to an system of equations or inequalities using elimination or substitution and justify the solution set
      • strategically use additive inverses, multiplicative inverses, and the distributive property to identify the solution set of the system
      • justify how each step maintains the equation’s balance
    • describe the meaning of a solution set in terms of the situation it models
    • substitute the solution to show it makes all equations in the system true 


Develop conceptual understanding:

viable, non-viable, intersection point, solution(s), solution set, substitution, elimination

Supporting terms to communicate:

function, system, equation, inequality, simultaneous, dependent, independent, domain, range, term, variable, constant, coefficient, equivalent, constraint

Core Resource
A core resource supports multiple days of instruction. COMING SOON!
    Instructional Routine: Connecting Representations
    These tasks are embedded within the instructional routine called Connecting Representations.