SAT Systems of Linear Equations Questions
Two lines at once, by substitution or elimination.
In short
- Systems of Linear Equations is part of Algebra, about 35% of the scored Math questions: 13 to 15 on every test.
- Math questions from all four areas are mixed in each module and arranged from easiest to hardest.
- System elimination is the trap Rivie's practice tests set most often in Systems of Linear Equations questions.
Common traps
Most common first, from Rivie's ten practice tests.
System elimination
Two equations to solve simultaneously by adding or subtracting; the wrong choice arises from a sign error during elimination or stops one step short.
The usual mistake: You scale one equation, forget to flip the sign on every term when subtracting, then 'solve' and get a confident wrong answer.
Infinite vs. unique solutions
A linear system has no solution if the lines are parallel (same slope, different intercepts), infinitely many if identical (same slope, same intercept), one solution otherwise.
The usual mistake: You solve the system algebraically and get '0 = 0', then pick 'no solution' instead of 'infinitely many'. The two outcomes are flipped from the equation that produces them.
Try a question
From Rivie's practice tests. Pick an answer to see why it is right or wrong.
3x + 2y = 14 x − y = 3 What is the value of x + y?
Video lessons
Free on YouTube, picked for this topic.