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Question

Solve the following systems of linear equations by using the method of elimination by equating the coefficients:
(i) 3x+2y=11
(ii)2x+3y=4

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Solution

The given systems of equations is
3x+2y=11 (i)
2x+3y=4 (ii)

Let us eliminate y from the given equations. The coefficients of y in the given equations are 2 and 3 respectively. The L.C.M. of 2 and 3 is 6. So, we make the coefficients of y equal to 6 in the two equations.

Multiplying (i) by 3 and (ii) by 2, we get
9x+6y=33 ...(iii)
4x+6y=8 ..(iv)

Subtracting (iv) from (iii), we get
5x=25x=5

Substituting x=5 equation in (i), we get
15+2y=112y=4y=2

Hence, the solution of the given system of equations is x=5,y=2.

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