Unit 4
Two conditions holding at once. The number of solutions is a geometric fact about whether the lines meet, are parallel, or coincide.
Lesson 4.1
A solution of a system satisfies every equation simultaneously. Substitution replaces one variable using an equivalent expression. Elimination combines equations to remove a variable. Choose the method that keeps arithmetic clear, then check the ordered pair in both original equations.
Lesson 4.2
Two lines may intersect once, be distinct and parallel, or coincide. These cases correspond to one solution, no solutions, or infinitely many solutions. In algebra, a false constant statement signals inconsistency, while an identity can signal equivalent equations.
Lesson 4.3
A linear inequality describes a half-plane. Draw a solid boundary when equality is allowed and a dashed boundary otherwise. Test a point not on the boundary to choose the correct side. The solution to a system is the overlap of the permitted half-planes.
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