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Systems of linear equations

Solve systems of linear equations graphically

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- 1. Systems of Linear Equations
- 2. Solving Systems of Equations Graphically
- 3. Definitions A system of linear equations is two or more linear equations whose solution we are trying to find. (1) y = 4 x – 6 (2) y = – 2 x A solution to a system of equations is the ordered pair or pairs that satisfy all equations in the system. The solution to the above system is (1, – 2).
- 4. Solutions Determine if ( – 4, 16) is a solution to the system of equations. y = – 4 x y = – 2 x + 8 (1) y = – 4 x 16 = – 4( – 4) 16 = 16 (2) y = – 2 x + 8 16 = – 2( – 4) + 8 16 = 8 + 8 16 = 16 Yes, it is a solution Example:
- 5. Solutions Determine if ( – 2, 3) is a solution to the system of equations. x + 2 y = 4 y = 3 x + 3 (1) x + 2 y = 4 – 2 + 2(3) = 4 – 2 + 6 = 4 4 = 4 (2) y = 3 x + 3 3 = 3( – 2) + 3 3 = – 6 + 3 3 = – 3 But… Example: So it is NOT a solution
- 6. Types of Systems <ul><li>The solution to a system of equations is the ordered pair (or pairs) common to all lines in the system when the system is graphed. </li></ul>( – 4, 16) is the solution to the system. y = – 4 x y = – 2 x + 8
- 7. Types of Systems <ul><li>If the lines intersect in exactly one point, the system has exactly one solution and is called a consistent system of equations . </li></ul>
- 8. Types of Systems <ul><li>If the lines are parallel and do not intersect, the system has no solution and is called an inconsistent system . </li></ul>y = 6 x y = 6 x – 5 There is no solution because the lines are parallel.
- 9. Types of Systems <ul><li>If the two equations are actually the same and graph the same line, the system has an infinite number of solutions and is called a dependent system . </li></ul>y = 0.5 x + 4 x – 2 y = – 8 There is an infinite number of solutions because each equation graphs the same line.

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