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Questions
Solve the following systems of equations:
`x + 2y = 3/2`
`2x + y = 3/2`
The given system of equation is
`x + 2y = 3/2` ..`.(i)
`2x + y = 3/2` ...(ii)
Let us eliminate y from the given equations. The Coefficients of y in the given equations are 2 and 1 respectively. The L.C.M of 2 and 1 is 2. So, we make the coefficient of y equal to 2 in the two equations.
Multiplying (i) by 1 and (ii) by 2, we get
`x + 2y = 3/2` ...(iii)
4x + 2y = 3 ....(iv)
Subtracting (iii) from (iv), we get
`4x - x + 2y - 2y = 3 - 3/2`
`=> 3x = (6 - 3)/2`
`=> 3x = 3/2`
`=> x = 3/(2 xx3)`
`=> x = 1/2`
Putting x = 1/2 in equation (iv), we get
`4 xx 1/2 + 2y = 3`
`=> 2 + 2y = 3`
`=> 2 + 2y = 3`
`=> 2y = 3- 2`
`=> y =1/2`
Hence, solution of the given system of equation is `x = 1/2` and `y = 1/2`
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