What you'll learn
Algebra is the largest domain on the Digital SAT Math section — roughly 35% of the questions. It covers linear equations, linear inequalities, systems of linear equations, and linear functions. Master this and you secure the biggest block of marks.
Linear equations in one variable
Solve by isolating the variable. Whatever you do to one side, do to the other.
- Example:
3x + 7 = 22→3x = 15→x = 5. - Watch for equations with variables on both sides:
5(x − 2) = 3x + 4→5x − 10 = 3x + 4→2x = 14→x = 7.
Linear functions and slope
The slope-intercept form is y = mx + b, where m is the slope and b the y-intercept.
- Slope between two points = (y₂ − y₁) / (x₂ − x₁).
- Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (e.g. 2 and −½).
- To find b, substitute a known point into y = mx + b.
Systems of equations
Two lines, two unknowns. Solve by substitution or elimination.
- Substitution: from
y = 2x, put intox + y = 9→x + 2x = 9→x = 3. - A system has no solution when the lines are parallel (same slope, different intercept) and infinite solutions when they are the same line.
Inequalities
Solve like equations, but flip the sign when you multiply or divide by a negative number.
4y + 9 ≤ 25→4y ≤ 16→y ≤ 4.
Word problems
Translate words into an equation: a fixed amount + a rate × quantity is the classic linear model. "$3 plus $2 per mile" → c = 2m + 3.
Exam strategy
- A calculator is allowed throughout SAT Math — but set up the algebra first, then compute.
- Plug answer choices back in if you're stuck (back-solving).
- Check whether the question asks for x, 3x, or something else — a common trap.
Common mistakes
- Forgetting to flip the inequality sign with a negative.
- Sign errors when expanding brackets.
- Answering for the wrong quantity.
Practise a few Algebra questions every day — familiarity with these patterns is the fastest route to a higher Math score.