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Pre-Algebra Ch. 8.2 Linear Equations in Two Variables Page 391 Vocabulary: Equation in two variables Solution of an equation in two variables Graph of an equation in two variables Linear Equation Function Form An EQUATION IN TWO VARIABLES is exactly what it implies: 2x - y = 5 To find the SOLUTION OF AN EQUATION IN TWO VARIABLES when the equation is in function form, you simply pick two numbers that make the equation true. Which of these ordered pairs is a solution to the equation? (1, -3) or (4, 7) Just plug those numbers into the equation and see if they make a true statement. 2(1) - (-3) = 5 is a true statement, but 2(4) - 7 = 5 is NOT a true statement. The answer is (1, -3) Your turn: Tell whether the ordered pair is a solution of + 2y = -8 1. (0,4) 2. (-2, 1) 3. (4, -12) 4. (10, -19) 3x You can use a table to help you determine solutions to equations with two variables. The number of pages p that Donald has left to write for his 30-page research paper depends on how many days d he writes 5 pages per day. This situation can be modeled by the equation p = 30 - 5d d p 0 30 1 25 2 20 You simply continue the chart in order to find the solution. How many days will it take Donald to write his paper? To graph a linear equation: The ordered pairs for the solution of y = 2x - 1 are: (1,1)(2,3)(3,5)(-1, -3)(-2,-5) The solution is a LINEAR EQUATION. Graph the equation: (1) y = 2x (2) y = 3x - 4 HOMEWORK: CH. 8.2 Page 394 #1 - 23 All Example 4: The solution could also be a horizontal or vertical line - you just have to make sure you plug in some numbers so you are sure before you graph: Name an ordered pair that is a solution for: (1) x = 1 (2) y = -4 You can say that a line is a function unless it is a VERTICAL LINE. An equation is said to be in FUNCTION FORM if it is solving for y. It will be easier to graph a solution if you put the problem in function form before graphing!! Write x + 2y = 6 in function form ANSWER: x + 2y = 6 -x + x + 2y = 6 - x 2y = 6 -x 1/2(2/1)y = 6(1/2) - (1/2)x y = 3 - 1/2(x) Write the equation x + 3y = 3 in function form, make a table of solutions, graph the solutions and tell whether the relations is a function: 2x - 3y = 3 2x-2x - 3y = 3 - 2x -1/3(-3/1)y = 3(-1/3) - 2x (-1/3) y = -1 + 2/3(x) Let x = 0 and y = -1 -1 = -1 + (2/3)0 (0,-1) Find other solutions and then graph HOMEWORK: CH. 6.2 Page 394 #24 - 31 #35 - 38, 42