Objective I will identify the number of solutions a linear system has using one of the three methods...
-
Upload
anis-green -
Category
Documents
-
view
248 -
download
0
Transcript of Objective I will identify the number of solutions a linear system has using one of the three methods...
Objective
• I will identify the number of solutions a linear system has using one of the three methods used for solving linear systems.
•If the graphs of the equations cross once, there will be one solution.
•If the graphs of the equations are parallel, there will be no solutions.
•If the graphs of the equations are the same line, there will be an infinite number of solutions.
Number of Solutions
Method 1: Function Form
Finding number of solutions Put equations in function form (isolate y; y = mx + b) Different slopes (m) - one intersection; one solution Same slope (m), different y-intercept (b) - parallel
lines, no solution Same slope (m) and y-intercept (b) - same line,
infinite solutions
Method 2: Substitution
Finding number of solutions Solve for one variable in one equation Substitute into other equation Equation is true - one solution Equation is false - no solution 0 = 0 - infinite solutions
Method 3: Linear Combinations
Finding number of solutions Multiply equations (if necessary) so one variable
has an opposite Add equations Solve Equation is true - one solution Equation is false - no solution 0 = 0 - infinite solutions
Example
Find the number of solutions.2x + y = 52x + y = 1Method 1: Function Formy = -2x + 5y = -2x + 1Same slope, different y-intercept - no
solution
Example Find the number of solutions.2x + y = 52x + y = 1Method 2: Substitutiony = -2x + 52x + (-2x + 5) = 12x - 2x + 5 = 10 + 5 = 15 ≠ 1Equation is false - no solution
Example Find the number of solutions.2x + y = 52x + y = 1Method 3: Linear Combinations2x + y = 5-2x - y = -1 0 ≠ 4
Equation is false - no solution
Guided Practice
Find the number of solutions.1. 8x + 4y = 16 3y = 6x - 152. -2y = -2x + 4 5y = 5x - 10
Independent Practice
Find the number of solutions.1. 6y = 12x + 18 -2x + y = 182. y = 14x - 3
-42x - 3y = -9