Systems of linear equations
- Course
- Algebra
- Question type
- Systems of two linear equations
- Practice
- 6 practice questions
- Language
- Vietnamese · English
About this lesson
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.
What you'll learn
- Read a system's solution as the intersection of two lines, however the SAT phrases it.
- Choose between substitution and elimination, or simply add the equations when the question asks for an expression.
- Decide between one, no or infinitely many solutions from coefficient ratios, even with an unknown constant k.
- Turn a word problem into a count equation and a value equation, then check it in Desmos.
Lesson contents
- Lesson goals
- 1. Systems and their solutions
- Key terms
- The picture behind it
- 2. Two methods: substitution and elimination
- Substitution
- Elimination
- When the question asks for an expression
- 3. How many solutions: one, none or infinitely many
- 4. Building a system from a word problem
- 5. Common traps
- 6. Speed strategies
This lesson is part of HOCSAT Learn
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