Week 2 - Systems of Linear Equations (Vocabulary Flashcards)

Vocabulary flashcards covering key concepts from Week 2 notes on systems of linear equations.

System of linear equations

A set of two or more linear equations in two variables; the solution is the pair (x,y) that satisfies every equation.

Solution to a system

A pair (x,y) that makes all equations in the system true.

Graphical solution

The solution found by graphing the equations as lines and identifying their intersection point.

Slope-intercept form

y = mx + b, a common form for linear equations used to graph lines.

Substitution method

A technique to solve a system by solving one equation for one variable and substituting that expression into the other equation.

Elimination method (addition)

A technique to solve a system by adding equations in order to cancel a variable and solve for the remaining variable.

Elimination with multiplication

A variant of elimination that multiplies one or both equations to create opposite coefficients before adding to eliminate a variable.

Dependent system

A system where the equations represent the same line (one is a multiple of the other); there are infinitely many solutions.

Infinitely many solutions

The set of solutions is unbounded (the equations are the same line), so every point on that line is a solution.

Inconsistent (no solution)

A system where the equations are parallel but not the same line, yielding no common solution.

One unique solution

The two lines intersect at exactly one point; the system has exactly one solution.

Word problem system

Modeling real-world scenarios with a system of equations to find quantities (e.g., sums, differences, prices).

Table-to-equations

Translating a table of values that represents a linear relationship into a system of equations and solving it.

Writing a system from a graph

Given a graph of two lines, write the equations that describe each line.