Systems of Linear Equations. Forms and Solutions.

Try to go through this lesson and find the answers for all these questions. You are going to be guided in a step by step process, with color clues, and minimizing long explanations in favor of visual representations of the solutions and concepts. Surely that you will like it!

Lesson's Content

 Lesson In PDF Format (no animations)

Lesson's Glossary

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 function:  The solution set graphed for the function in the given domain.

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.

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.

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.

Interactive Algebraic Applets

Try the interactive algebraic applet below. You may view the

parameters of the slope, and the y-intercept (0,b) by dragging the sliders.

Parallel lines are defined as lines in the same plane, and with the same

slope. In this case the plane is the coordinate plane. Interact with

this algebraic applet to visualize how lines are parallel when you

manipulate the y-intercept, or the slope.

Perpendicular lines have slopes that are the negative reciprocal of each other.

This interactive algebraic applet allows you to drag the point in the slider

to view several instances of perpendicular lines. Observe their rise, and run

values, and their respective slopes.

Vocabulary Puzzle

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