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Systems of Linear Equations: Elimination Method
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Systems of Linear Equations: Elimination Method
In the 'elimination' method for solving simultaneous equations, two equations are simplified by adding them or subtracting them. This eliminates one of the variables so that the other variable can be found.
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Example: Solve the following simultaneous equations by using the elimination method:
      2x + 3y = 1
      3x + 2y = 4
Solution: The given system of equations is
      2x + 3y = 1 ...(i)
      3x + 2y = 4 ...(ii)
eliminate x from the given equations. The coefficients of x in the given equations are 2 and 3 respectively. The l.c.m. of 2 and 3 is 6. So,  make both the coefficients equal to 6.
Multiplying both sides of equation (i) by 3 and equation (ii) by 8, we get
      6x + 9y = 3 ...(iii)
      6x + 4y = 8 ...(iv)
Subtracting (iv) from (iii), you will get
5y = -5 y = -1
Putting y = -1 in (i), 
you get 2x + 3y = 1
2x + 3 * (-1) =1
2x = 3 + 1 
x = 4/2 = 2 
Hence, the solution of the given system of equations is x = 2, y =-1.
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