Week 6 Only 3 weeks left to go! 11.1 1, 11, 21, 31, 41, 47, 55, 59, 65, 69 System of Linear Equations ● Two or more linear equations made up of two or more variables ● Value of the variables must satisfy all equations in the system of linear equations ● Consistent System ○ ○ ○ Has at least one solution Independent ■ Has a single solution Dependent ■ Equations have same slope and intercepts ■ Infinite number of solutions (represent the same line) ● Inconsistent System ○ ○ Equations represent parallel lines Same slope, different y-intercepts Example 1. Determine whether the ordered pair (5,1) is a solution to the given system of equations. x + 3y = 8 2x - 9 = y Step 1. Substitute points into equations X + 3y = 8 → 5 + 3(1) = 8 → 8 = 8 2x - 9 = y → 2(5) - 9 = 1 → 1 = 1 Step 2. If equations equal, it is a solution 8 = 8 and 1 = 1 , so true for both and is a solution of the system of equations Solving by Graphing…. Example 2 Solve the following system of equations by graphing. Identify the type of system. 2x + y = -8 x - y = -1 Step 1. Solve Each Equation for y 2x + y = -8 → y = -2x - 8 x - y = -1 → -y = -x - 1 → y=x+1 Step 2. Graph equations → Step 3. Confirm that the point of intersection solves the given equations 2(-3) + (-2) = -8 → -8 = -8 (-3) - (-2) = -1 → -1 = -1 Step 4. Identify type of system → Independent (single solution) Solve by Substitution… Example 3 -x + y = -5 2x - 5y = 1 Step 1. Solve first equat ...
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