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# Systems of equations-types of solutions

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Types of solutions in Systems of Equations

Types of solutions in Systems of Equations

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### Transcript

• 1. Types of Solutions
• 2. A System of Linear Equations means two of more linear equations. If the two lines intersect, then the point of intersection is called the solution.
• If the graphs have a solution, the system is consistent.
• If the system has one solution, then it is consistent and independent
• If the system has infinite solutions, then it is consistent and dependent
If the graphs do not intersect, the system has no solution and is inconsistent.
• 3. The system has exactly 1 solution. Systems have 1 and only 1 solution when the two lines have different slopes. This system is consistent and independent . Solutions is (20, 4)
• 4. System has infinite solutions A system of equations has infinite solutions if the two lines are exactly the same. They have the same slope and y-intercept. The system is consistent and dependent Example Line 1: y= x +2 Line 2: y= 3x + 6 If you divide line 2 by 3, It will be exactly the same as line 1 The graph of the two lines are exactly the same.
• 5. System has no solutions System has no solutions when the lines are parallel. The equations have the same slope with different y-intercepts. The system is inconsistent . Example Line 1: y = 2x + 1 Line 2: y = 2x - 1 The lines are parallel to each other.