SAT Math · 33% of the test
Heart of Algebra
Heart of Algebra covers linear equations, linear inequalities, systems of two linear equations, and the relationship between linear functions and their graphs. It is the largest single content category on the SAT Math section by item count.
What's actually tested
Roughly a third of every SAT math form lives here. Items range from a one-step equation buried inside a word problem to a system of two equations whose intersection point you must interpret in the context of a real-world scenario. The most common item shapes are: solving a single linear equation for a variable, building a linear equation from a description, interpreting the slope or y-intercept of a linear model in context, and solving a system of two linear equations either algebraically (substitution or elimination) or graphically.
Subtopics
Click any subtopic to see filed practice questions, worked solutions, and a short tactical guide.
Linear equations in one variable
Solving ax + b = c style equations and isolating a variable.
Linear functions and their graphs
Slope, intercepts, and reading linear graphs in context.
Systems of two linear equations
Solving 2-by-2 systems by substitution, elimination, or graphing.
Linear inequalities and systems of inequalities
Solving inequalities and reading shaded regions in the plane.
Sample practice questions in this topic
- Easy Linear equations in one variable If 7x − 2 = 26, what is the value of x?
- Easy Linear equations in one variable If 5x + 9 = 54, what is the value of x?
- Medium Linear equations in one variable If 5x + 10 = 55, what is the value of x?
- Medium Linear equations in one variable If 5x + 12 = -38, what is the value of x?
- Medium Linear equations in one variable If 6x + 1 = 25, what is the value of x?
- Hard Linear equations in one variable If 5x + 10 = 35, what is the value of x?
- Easy Linear equations in one variable If 3x + 8 = -19, what is the value of x?
- Easy Linear equations in one variable If 2x − 1 = 11, what is the value of x?
- Medium Linear equations in one variable If 4x − 10 = 26, what is the value of x?
- Medium Linear equations in one variable If 7x + 8 = -34, what is the value of x?
- Medium Linear equations in one variable If 2x + 10 = 2, what is the value of x?
- Hard Linear equations in one variable If 6x + 1 = 7, what is the value of x?
See all 56 questions in Heart of Algebra →
How students lose points here
The most common loss-of-points patterns here are arithmetic sign errors when distributing a negative across parentheses, misreading which variable a question asks for in a system, and confusing the slope with the y-intercept when interpreting a linear model in context. The good news: nearly every common mistake on this topic comes from one of three or four recurring patterns. Spend an hour reviewing those patterns and your accuracy on this topic typically jumps two or three percentage points immediately, which on a balanced test is worth ten to twenty scaled score points depending on your band.
How to study this topic
Drill subtopic by subtopic until each shape is automatic. Linear systems specifically reward students who recognize within five seconds whether substitution or elimination will be faster — that decision matters as much as the algebra itself. A reasonable session looks like fifteen practice items, untimed, with you reading the worked solution after every one — even the questions you got right, because being right by accident teaches nothing. After two or three such sessions, attempt a timed mini-set of ten items. If your accuracy stays above 80%, move on. If it doesn't, drill the lowest-accuracy subtopic for another session before you push forward.