Systems of linear equations (Systems of two linear equations)

강의 소개

Systems of two linear equations in two variables: the solution as an intersection point, substitution and elimination, one / no / infinitely many solutions from the coefficients, setting up a system from a word problem, and solving fast with Desmos.

On the Digital SAT, systems of two linear equations are their own skill in the Algebra domain and show up in both math modules. A question may hand you the two equations, show two intersecting graphs, or hide the system inside a word problem about tickets, prices or quantities; some questions skip the solution entirely and ask which constant makes the system have no solution or infinitely many.

Points are usually lost at the very end rather than in the algebra: finding x when the question wants x + y, multiplying an equation but not its right side, or calling a system inconsistent as soon as the slopes match without checking the constants. This lesson moves from what an intersection means to the two solving methods, then to reading the number of solutions straight from the coefficients, with Desmos tricks for checking an answer in seconds. It ends with 6 self-graded practice questions, each with a full explanation.