From 2ada583a44c6f99c40e3908a08092b421a921890 Mon Sep 17 00:00:00 2001 From: Soup <39444003+magicalsoup@users.noreply.github.com> Date: Sat, 13 Apr 2019 11:15:36 -0400 Subject: [PATCH] Update Final_Exam_Study_Sheet.md fixed formatting --- Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md | 76 +++++++++---------- 1 file changed, 38 insertions(+), 38 deletions(-) diff --git a/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md b/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md index 78cfebe..7df1de7 100644 --- a/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md +++ b/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md @@ -541,46 +541,46 @@ # Ways to solve Systems of Equations - 1. Subsitution - - Here we eliminate a variable by subbing in another variable from another equation - - We usually do this method if a variable is easily isolated - - Example: - - ``` - y = x + 10 (1) - x + y + 34 = 40 (2) - ``` - We can sub (1) into (2) to find ```x```, then you the value of ```x``` we found to solve for ```y``` - ```x + (x + 10) + 34 = 40``` - ```2x + 44 = 40``` - ```2x = -4``` - ```x = -2``` - Then solve for ```y``` - ```y = -2 + 10``` - ```y = -8``` + ## 1. Subsitution + - Here we eliminate a variable by subbing in another variable from another equation + - We usually do this method if a variable is easily isolated + - Example: + - ``` + y = x + 10 (1) + x + y + 34 = 40 (2) + ``` + We can sub (1) into (2) to find ```x```, then you the value of ```x``` we found to solve for ```y``` + ```x + (x + 10) + 34 = 40``` + ```2x + 44 = 40``` + ```2x = -4``` + ```x = -2``` + Then solve for ```y``` + ```y = -2 + 10``` + ```y = -8``` - 2. Elimination - - Here we eliminate a variable by basically eliminate a variable from an equation - - We usually use this method first when the variables are not easily isolated, then use subsitution to solve - - Example: - - ``` - 2x + 3y = 10 (1) - 4x + 3y = 14 (2) - ``` - We can then use elimination - ``` - 4x + 3y = 14 - 2x + 3y = 10 - ------------ - 2x + 0 = 4 - x = 2 - ``` - Then sub the value of ```x``` into an original equation and solve for ```y``` - ```2(2) + 3y = 10``` - ```3y = 6``` - ```y = 2``` + ## 2. Elimination + - Here we eliminate a variable by basically eliminate a variable from an equation + - We usually use this method first when the variables are not easily isolated, then use subsitution to solve + - Example: + - ``` + 2x + 3y = 10 (1) + 4x + 3y = 14 (2) + ``` + We can then use elimination + ``` + 4x + 3y = 14 + 2x + 3y = 10 + ------------ + 2x + 0 = 4 + x = 2 + ``` + Then sub the value of ```x``` into an original equation and solve for ```y``` + ```2(2) + 3y = 10``` + ```3y = 6``` + ```y = 2``` -3. Graphing -- we can rewrite the equations into ```y-intercept form``` and then graph the lines, and see where the lines intersect (P.O.I), and the P.O.I is the solution +## 3. Graphing + - we can rewrite the equations into ```y-intercept form``` and then graph the lines, and see where the lines intersect (P.O.I), and the P.O.I is the solution ## Solving Systems of Linear Inequalities - Find the intersection region as the ```solution```.