“Equations and Inequalities” Vocabulary for Module 4 “Equations and Inequalities”

Addition Property of Equality In an equation, any amount can be added to one side, provided an equivalent amount is added to the other side. If a=a, the a + b = a + b.

Subtraction Property of Equality In an equation, any amount can be subtracted from one side, provided an equivalent amount is subtracted from the other side. If a=a, the a - b = a - b.

Multiplication Property of Equality In an equation, any amount can be multiplied on one side, provided an equivalent amount is multiplied on the other side. If a=a, the ab = ab.

Division Property of Equality In an equation, any amount can be divided on one side, provided an equivalent amount is divided on the other side. If a=a, the a ÷ b = a ÷ b.

Algebraic Expression A mathematical phrase involving at least one variable and sometimes numbers and operation symbols

Coefficient A number multiplied by a variable in an Algebraic Expression. 4x 17y 42b

Cartesian Coordinate Plane a coordinate system that specifies each point uniquely in a plane by a pair of numericalcoordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

 Coordinates Each point graphed can be represented by a unique pair of numbers called an ordered pair. The numbers in that ordered pair are called the coordinates.

Equation A mathematical sentence that contains an equals sign.

 Inequality Any mathematical sentence that contains the symbols >(greater than), <(less than), <(less than or equal to), or >(greater than or equal to).

Origin The point of intersection of the vertical and horizontal axes of a Cartesian plane. The coordinates of the origin are (0, 0).

Quadrant One of the four regions on a Coordinate plane formed by the intersection of the x- axis and the y-axis.

Simultaneous Equation equations involving two or more unknowns that are to have the same values in each equation

Solution A number (or ordered pair of numbers, or set of numbers) that produces a true statement when substituted for the variable(s) in an equation or inequality.

 Substitution To replace one element of a mathematical equation or expression with another.

System of Linear Equations Two or more equations that together define a relationship between variables usually in a problem situation. It can have no solution, one solution, or many solutions.

Variable A letter or symbol used to represent a number.

X-axis The horizontal number line on the Cartesian coordinate plane.

 x-coordinate The first number of an ordered pair; the position of a point relative to the vertical axis.

Y-axis The vertical number line on the Cartesian coordinate plane.

 y-coordinate The second number of an ordered pair; the position of a point relative to the horizontal axis.