# Key Terms Chapter 04: Systems of Linear Equations

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Example and Directions
Words (or words that have the same definition)The definition is case sensitive(Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages](Optional) Caption for Image(Optional) External or Internal Link(Optional) Source for Definition
(Eg. "Genetic, Hereditary, DNA ...")(Eg. "Relating to genes or heredity")The infamous double helix https://bio.libretexts.org/CC-BY-SA; Delmar Larsen
Glossary Entries
break-even pointThe point at which the revenue equals the costs is the break-even point; $$C(x)=R(x)$$.
coincident linesCoincident lines have the same slope and same $$y$$-intercept.
complementary anglesTwo angles are complementary if the sum of the measures of their angles is $$90$$ degrees.
consistent and inconsistent systemsConsistent system of equations is a system of equations with at least one solution; inconsistent system of equations is a system of equations with no solution.
cost functionThe cost function is the cost to manufacture each unit times $$x$$, the number of units manufactured, plus the fixed costs; $$C(x) = (\text{cost per unit})x+ \text{fixed costs}$$.
determinantEach square matrix has a real number associated with it called its determinant.
matrixA matrix is a rectangular array of numbers arranged in rows and columns.
minor of an entry in a $$3×3$$ determinantThe minor of an entry in a $$3×3$$ determinant is the $$2×2$$ determinant found by eliminating the row and column in the $$3×3$$ determinant that contains the entry.
revenueThe revenue is the selling price of each unit times $$x$$, the number of units sold; $$R(x) = (\text{selling price per unit})x$$.
row-echelon formA matrix is in row-echelon form when to the left of the vertical line, each entry on the diagonal is a $$1$$ and all entries below the diagonal are zeros.
solutions of a system of equationsSolutions of a system of equations are the values of the variables that make all the equations true; solution is represented by an ordered pair $$(x,y)$$.
solutions of a system of linear equations with three variablesThe solutions of a system of equations are the values of the variables that make all the equations true; a solution is represented by an ordered triple $$(x,y,z)$$.
square matrixA square matrix is a matrix with the same number of rows and columns.
supplementary anglesTwo angles are supplementary if the sum of the measures of their angles is $$180$$ degrees.
system of linear equationsWhen two or more linear equations are grouped together, they form a system of linear equations.
system of linear inequalitiesTwo or more linear inequalities grouped together form a system of linear inequalities.