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Elimination Method:
Intersecting Lines: Example: Solve the system of linear equations: 3x + 2y = 4  Equation 1 5x  2y = 8  Equation 2 Solution: Adding both equations, to eliminate y, we get 3x + 2y = 4 equation 1 5x  2y = 8  equation 2. Adding equations. 8x = 12 x = 12/8 = 3/2. By back substituting we can solve for y. substituting the value of x in equation 1 we have 3x + 2y = 4 3(3/2) + 2y = 4 y = 1/4 The solution of the two equations is x = 3/2 and y = 1/4
Example:
Verification:
Example:
Verification: Parallel Lines: Method of Elimination: Nosolution Case Example: Solve the system of linear equations: x  2y = 3  Equation 1 2x + 4y = 1  Equation 2 Solution: Here we obtain the coefficients that differ only in sign by multiplying equation 1 by 2 . 2(x  2y = 3)  Equation 1 2x + 4y = 1  Equation 2 The equations we get are: 2x  4y = 6  Equation 1 2x + 4y = 1  Equation 2 Adding both equations, to eliminate y, we get  0 = 7  False statement Since there are no values of x and y for which 0 = 7 we can conclude that the system is inconsistent and has no solution. In other words the two lines do not intersect they are parallel lines Two lines Coincide: Method of Elimination: Manysolution Case Example: Solve the system of linear equations: 2x  y = 2  Equation 1 4x  2y = 2  Equation 2 Solution: To obtain the coefficients that differ only in sign by multiplying equation 2 by 1/2 . The equations we get are: 2x  y = 2  Equation 1 1/2( 4x 2y = 2)  Equation 2 2x + y = 1 Adding both equations, to eliminate y, we get  0 = 0 Since the two equations turn out to be equivalent or have the same solution set, the system has infinitely many solutions. In other words the two lines coincide Directions: Solve for the variables using the method of Elimination. Also write at least 5 examples of your own. 
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