# Systems of Linear Inequalities in Two Variables. Graphing and Solution.

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Lesson's Content

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Lesson's Glossary

Absolute value:  Distance of a number from zero on a number line. The distance is taken as positive all the time. For a variable: If x < 0 then –a; if x>=0 then a.

Equivalent system:  A system of equations having the same solution set as another system.

Graph of an equation in two variables:  All the points that may be graph from the solution set of the equation.

Graph of a number:   The location of a point paired with a number in the number line.

Graph of an ordered pair:  The location in the coordinate plane associated with an ordered pair of real numbers.

Inequality:  A statement formed by placing an inequality symbol between numerical or variable expressions.

Inequality symbols:  Symbols used to show the order of two real numbers.

Sides of an inequality:   The two expressions at both sides of the inequality sign in an inequality. Left and right.

Linear equation:   Any equation with all exponents = 1 regardless of the form the equation is represented.

Linear equation in two variables:   All equivalent equations to the one in the form of ax + by = c, where a, b, and c are in the set of the real numbers and a and b can't be zero at the same time. The graph is a straight line.

Linear function:  A function of the form: f(x) = mx + b.

Ordered pair:   In a coordinate plane is the location of a point.

Ordinate:  The y-coordinate in an ordered pair of the coordinate plane.

Origin:   The location of the zero point in a number line.

Parallel lines:   Lines with the same slope. Lines in the same plane that don't intersect.

Perpendicular lines:   Lines that intersect or cross at right angles. Multiplying the slopes of perpendicular lines always yield -1.

Plot a point:   Locating and graphing an ordered pair of real numbers in the coordinate plane.

Point-slope form of an equation:  Y - Y1 = m(X-X1), where m is the slope and (X1 , Y1) the point for which the line goes through.

Slope of a line: The measure of how steep a line is. The change in y (rise) divided by the change in x (run). Slope = m

Slope-intercept form of an equation:   The equation of a line in the form y = mx + b, where m represents the slope, and be represents the y-intercept.

Solution of an equation in two variables:  Any ordered pair of real numbers that makes the sentence true.

Solution of a system of two equations in two variables:   Ordered pair that when replaced in the equations produces a true statement for both equations.

Solve a system of two equations in x and y:   Finding all ordered pairs (x,y) which make both equations in the system true.

Standard form of a linear equation:   ax + by = c, where a, b, and c are integers and a and b are not both zero.

x-intercept:  The x-coordinate of a given point for which the graph intersects the x-axis.

y-intercept: The y-coordinate of a given point for which the graph intersects the y-axis.

Vocabulary Highlights

Slope of a line: The measure of how steep a line is. The change in y (rise) divided by the change in x (run). Slope = m

Slope-intercept form of an equation:   The equation of a line in the form y = mx + b, where m represents the slope, and be represents the y-intercept.

Point-slope form of an equation:  Y - Y1 = m(X-X1), where m is the slope and (X1 , Y1) the point for which the line goes through.

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