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Warm Up Write the following equations in slopeintercept form. 1) 3y = 6x + 24 2) 2x + y = 20 3.What is the slope of the line containing the points (2,2) and (5,5)? Standard Form Ax + By = C Solve for y to rewrite the equation in slope-intercept form How do you graph an equation using the slope and the y-intercept? y= mx + b When all else fails, you can always make a table and simply plot points A solution for a single equation is ANY point that lies on the line of that equation What is a system of equations? Let’s look at some examples to better understand YES NO X+3=5 YES NO X+6 ≥ -3 Z+Y < 5 YES YES NO Y=4 Yes or No? x+y+z= 5 Yes or No? Yes or No? X-1> -9x What is a system of equations? Video response What is a solution to a system of equations? Video response Think-Ink-Share How do you know that (0,0) is not the solution to the system of equations : 3x+y=5 and 2x-1=4 Systems of Linear Equations • A system of equations is a set of two or more equations with the same variables. • A solution to a system of equations is a set of values for the variables that satisfy all the equations • The number of equations must match the number of variables • A solution for a single linear equation is any point that lies on the line for that equation. A solution for a system of linear equations is any point that lies on each line in the system. Three Methods for Solving a System of Equations • Graphing • Substitution • Elimination ( or Linear Combination) If I have two lines, is it possible for them to intersect at more than one point? How can you find the solutions of a system by looking at the graphs? Systems Applet EQUATION 1 EQUATION 2 Solution Sketch the graphs Exactly one solution y x Consistent and Independent System Exactly one solution y x Infinitely many solutions y x Consistent and Dependent System Infinitely many solutions y x NO solution y x Inconsistent and Independent System NO solution y x You Try Summary • How is a system of equations like an equation? How is it different? • How can you look at the graph of a system to find the solution? Assign Homework: Clear desk for Ticket Out the Door