Unit 9: Expressions and Equations (Systems of Equations)

A system of linear equations consists of two linear equations in two variables.

The solution to a system of two linear equations corresponds to the point of intersection (x,y) of their graphs because that point satisfies both equations simultaneously.

Systems of linear equations can have exactly one unique solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (the same/coinciding line).

Parallel lines share the same slope but have different y-intercepts, meaning they will never intersect and thus have no solution.

Real-world problems involving two changing conditions or constraints can be modeled mathematically using a system of linear equations.

Graph proportional and non-proportional linear equations on a coordinate plane to find or estimate the point of intersection for a system.

Solve systems of two linear equations in two variables algebraically using substitution and elimination methods.

Solve simple systems by inspection (e.g., recognizing that 3x+2y=5 and 3x+2y=6 can have no solution because 3x+2y cannot simultaneously equal two different constants).

Translate real-world scenarios and mathematical problems into a cohesive system of two linear equations in two variables.

Verify algebraic solutions by substituting the derived ordered pair back into both original equations to check for accuracy.

Performance Tasks

SBA Interim Assessment

Unit Test