Curriculum placement
Algebra 1. This describes the skill, not a learner estimate.
Systems that model two constraints
Model simultaneous constraints with equations and inequalities
Problem types
- Write a system from a table, graph or story
- Solve a two-variable model
- Meet every constraint
- Use one count to find another, then combine
- Write one equation for two quantities with a known total and cost
Builds on
- Systems of linear equations
- Solving inequalities
- Linear equations from constraints · Earlier idea
One linear model extends to two models compared together, where the solution is when they agree.
- Regions defined by inequalities · Useful idea
The overlap of half-plane regions is the set of feasible choices in a constrained model.
- Naming the quantities in a model · Useful idea
A system of equations for a situation needs each quantity defined first, with a variable and a unit for each.
- Modeling density · Useful idea
Mixing two materials of known densities to get a given total mass and volume is solved with a system of equations.
- Inequalities on a number line · Useful idea
A set of limits in a situation is a system of inequalities, and a solution satisfies all of them.
- Multi-step word problems · Useful idea
Two multistep stories about the same unknown are written together as a system of equations.
Leads to
- Designs that meet geometric constraints
- Solving a linear and a nonlinear equation together · Extend the idea
Setting up a system from a situation extends to systems with a curve, where solutions are intersection points.
- A system written as a matrix equation · Extend the idea
A system from a situation is written as a matrix equation whose solution is found with an inverse.
Related skills
- Why elimination keeps the same solutions · Shared foundations
- Linear equations with letter coefficients · Shared foundations
Open the interactive map to explore lessons and skill connections.