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

Many times we are puzzled with a linear inequality in two variables, and asking ourselves: Where should I shade? Above, or below? How Do I find out the solution for several of these inequalities together? What happens to the graph of an absolute value equation if I change the coefficients, and/or the constant term? To help yourself would be advisable to go over the definitions given by scrolling down the screen. Down there is also a section highlighting forms of a linear equation: Slope-Intersection, Point-Slope and Slope definition. Optionally, throughout the lesson you might wish to highlight or write useful notes using the MARKER TOOLS menu at the top of the screen.

Check this lesson. You will be greatly satisfied for the way in which it explains all the above questions and answers them in a very easy to follow manner. Go ahead, do your best!

Lesson's Content

Lesson In PDF Format (no animations)

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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 of a Line

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.

Slope 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.

Point Slope Form>

 

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