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

- analyze terms in the equations of a system to strategically rewrite them in 1 variable

**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