Elimination Method of Finding Solution of a Pair of Linear Equations
Solve the fol...
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=25⇒x=5
Substituting x=5 equation in (i), we get 15+2y=11⇒2y=−4⇒y=−2
Hence, the solution of the given system of equations is x=5,y=−2.