Unit 1 · 4 lessons
Linear Systems
Find the point where two lines meet: solve systems of two linear equations by graphing, substitution and elimination, tell when a system has one, no or infinitely many solutions, and use systems to solve real problems about money, mixtures and rates.
- 42 practice questions
- 32 flashcards
- 2 interactive lessons
Lessons
- 1Solving Linear Systems by GraphingA linear system is two linear equations considered together. Its solution is the ordered pair that makes both equations true, which is where the two lines cross on a graph. Learn to check a solution, solve by graphing, and tell when a system has one, no or infinitely many solutions.Interactive10 questions
- 2Solving by SubstitutionSubstitution turns two equations in two variables into one equation in one variable: isolate a variable in one equation, replace it in the other, solve, then back-substitute. It gives exact answers, even fractions, and shows when a system has no solution or infinitely many.11 questions
- 3Solving by EliminationElimination adds or subtracts the two equations so that one variable cancels. Multiply one or both equations first so a pair of coefficients match, then solve, back-substitute and check. Learn when elimination beats substitution or graphing.Interactive10 questions
- 4Problems Using Linear SystemsTurn a word problem with two unknowns into a linear system: define the variables, organize the facts in a table, write one equation per fact, solve, and verify the answer against the original words. Investments, mixtures, tickets, speeds with a current, and comparing plans.11 questions