30S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Using Winplot to Solve Linear Systems Lesson: SLE-L4 Using Using Winplot to Solve Linear Systems Learning Outcome B-1 SLE-L4 Objectives: Solve systems of equations using WinPlot

30S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Using Winplot to Solve Linear Systems Lesson: SLE-L4 Winplot will be demo’ed for you in class. Take note of the following: 2-dim means 2-variable equations How to enter an equation into y=f(x) How to edit an equation (inventory palette) Modifying your grid’s appearance (axes, ticks, etc.) Modifying your window location and scope Displaying an equation on the graph (equa on inventory palette) Winplot Demo 1

30S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Using Winplot to Solve Linear Systems Lesson: SLE-L4 y = mx + b, slope-intercept form Remember that for a line written in the form y = mx + b, m represents the slope, and b represents the y-intercept The x-intercepts are called zeroes, or roots, or solutions to single equations. Solutions to systems of equations are the point(s) where the two lines intersect. Theory – Slope y-intercept form

30S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Using Winplot to Solve Linear Systems Lesson: SLE-L4 Winplot will be demo’ed for you in class. Take note of the following: How to use trace How to find zeroes How to find the y-intercept How to generate a Table of Values (horizontal extremes determine start and end values in steps) Solve the equation 3x - 6 = 0 using WinPlot. Use WinPlot to find the zero of the equation -7.5x + 30 = 0. Theory – Substitution Method

30S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Using Winplot to Solve Linear Systems Lesson: SLE-L4 When a pair of linear equations is used together, the pair is called a linear system. Each equation produces a straight line when it is graphed. The lines may or may not intersect. Solving the system of linear equations means finding the point of intersection of the lines. The point is written as an ordered pair (x, y). Theory – Systems

30S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Using Winplot to Solve Linear Systems Lesson: SLE-L4 Imagine two straight lines on a coordinate plane. In how many ways can they meet? Theory – Solution Options They can cross and meet at one point. One solution Consistent or Independent system They can never meet if the lines are parallel. No solution Inconsistent system They can meet an infinite number of times, if they are the same line. Infinite number of solutions Dependent System

30S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Using Winplot to Solve Linear Systems Lesson: SLE-L4 Solve the following systems of equations using the Intersection dialogue box. y = x + 4 2y = x + 3 y = 2.5x - 3 y = 2.5x + 2 Theory – Substitution Method 2y = 6x + 4 y = 3x + 2 2y + x = 10 3y + 2x = 14