Systems of Linear Equations — SAT Math Explained
A set of two or more linear equations sharing the same variables. The solution is the point (or points) where all equations are simultaneously satisfied — where all lines intersect.
The Core Idea
Real situations often have multiple constraints at once. A system lets you find a single value that satisfies all conditions simultaneously, not just one at a time.
Key Vocabulary
Two or more equations considered together
An ordered pair (x, y) that makes ALL equations in the system true
Has at least one solution
Has no solution — lines are parallel
Has infinitely many solutions — lines are identical
Types Of Systems
The two lines intersect at exactly one point
The lines are parallel — same slope, different intercepts — they never meet
Both equations describe the same line
Methods Overview
Graphing: Plot both lines and identify intersection — best for visual understanding
Substitution: Solve one equation for one variable, plug into the other — best when a variable is already isolated
Elimination: Add/subtract equations to eliminate a variable — best when coefficients align
Real World Application
Finding where supply meets demand in economics, determining when two vehicles are at the same location, comparing two pricing plans
How This Connects to Other Topics
Substitution and elimination are the two main algebraic methods and each is its own topic
Practice: Systems of Linear Equations
5 SAT-style questions. Select your answer and get an instant explanation.
Is (2, 5) a solution to the system: y = 2x + 1 and y = x + 3?
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