Quizzes, exams, and flashcards about Algebra: Algebra 1 — linear equations, systems and inequalities.
← SAT
Linear equations, linear functions, systems and inequalities — ≈35% of the Math section, 13 to 15 questions, and jointly with Advanced Math it is 70% of your Math score.
Five skill points, all of them linear:
Very few of these questions are hard algebra. Most of them are ordinary algebra wrapped in a sentence, and the failure is in the wrapping: setting up the equation, not solving it.
Two habits fix most of that.
Define your variable in words before you write anything. "Let c be the number of cars" costs three seconds and prevents the single most common error on this domain, which is solving correctly for the wrong quantity. The SAT knows about that error and puts the value of the other variable among the choices.
Read the last line of the question again before you answer. It may ask for x, or for 2x, or for the price after the increase rather than the increase. Every one of those appears among the options.
No solution or infinitely many. Two linear equations describe the same line (infinitely many solutions), parallel lines (none), or intersecting lines (exactly one). A question that gives you a coefficient as an unknown and asks for the value that produces no solution is asking about parallel lines — same slope, different intercept — and it is much faster to answer that way than by solving anything.
Interpretation questions. In the equation C = 45h + 120, what does 120 represent? No calculation at all: the constant is the value when the variable is zero, the coefficient is the rate of change. These are free marks if you read them as structure and slow ones if you start substituting.
You have a graphing calculator throughout the Math section, and on this domain it is genuinely powerful: a system of two linear equations can be graphed and the intersection read off, and an "no solution" question can be checked visually in seconds. But the questions are written to be solvable without it, and reaching for it on a question that needs one line of algebra costs more time than it saves.
