Algebra is the biggest slice of the SAT Math section: linear equations, systems, inequalities, and interpreting linear relationships. At the 1500+ level, the content is rarely hard — speed and accuracy are what separate scores.
Golden rule of systems: if one variable is already isolated (or easy to isolate), substitute. If the equations line up neatly, add/subtract to eliminate. Pick the faster path per problem.
What to have automatic
- Slope = (y₂ − y₁)/(x₂ − x₁); slope-intercept form y = mx + b, where b is the y-value at x = 0.
- Solutions of a linear system = the point where the lines meet. No solution = parallel (same slope, different intercept). Infinitely many = the same line.
- When you multiply or divide an inequality by a negative, flip the sign. This is the #1 careless error.
Word-problem move: Define the variable in words first ("let m = number of months"), then translate each sentence into one equation. Set expressions equal when the problem says "the same."