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Algebra1: Solving a System of Equations which is Reducible to a System of Simultaneous Linear Equations
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Solving a System of Equations which is Reducible to a System of Simultaneous Linear Equations
Simultaneous equations are a set of equations containing multiple variables. This set is often referred to as a system of equations. A solution to a system of equations is a particular specification of the values of all variables that simultaneously satisfies all of the equations.
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Example: Solve:1/(2x) - 1/y = -1,
1/x + 1/(2y) = 8,
where x 0, y 0
Solution: Taking 1/x = u and 1/y = v, then given equations become:
u/2 - v = -1 => u - 2v = -2 ...(i)
u + v / 2 = 8 => 2u + v = 16 ...(ii)
Let us eliminate u from equations (i) and (ii). Multiplying equation (i) by 2, you get
2u - 4v = -4 ...(iii)
2u+ v = 16 ...(iv)
Subtracting (iv) from (iii), you get:
-5v = -20 => v = 4
Putting v = 4 in equation (i), you get
Hence x = 1/u = 1/6 and y = 1/v = 1/4
So, the solution of the given system of equation is x = 1/6, y = 1/4.
 
   
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