Question

Solve for m and n in the equations 4m + 3n + 24= 0 and 7m – 2n = -13, hence find 3m – 4n

Answer 1

$\large\underline{\sf{Solution-}}$

The given pair of linear equations are

$\rm :\longmapsto\:4m + 3n = - \: 24 - - - (1)$

and

$\rm :\longmapsto\:7m - 2n = - 13 - - - (2)$

Now, we use elimination method to solve these system of linear equations.

Multiply equation (1) by 2, we get

$\rm :\longmapsto\:8m + 6n = - \: 48 - - - (3)$

Now, Multiply equation (2) by 3, we get

$\rm :\longmapsto\:21m - 6n = - 39 - - - - (4)$

On adding equation (3) and equation (4), we get

$\rm :\longmapsto\:29m = - 87$

$\bf\implies \:m \: = \: - \: 3$

On substituting m = - 3, in equation (1), we get

$\rm :\longmapsto\:4( - 3) + 3n = - \: 24$

$\rm :\longmapsto\: - 12+ 3n = - \: 24$

$\rm :\longmapsto\: 3n = - \: 24 + 12$

$\rm :\longmapsto\: 3n = - \: 12$

$\bf\implies \:n \: = \: - \: 4$

Verification :-

Consider equation (2), we have

$\rm :\longmapsto\:7m - 2n = - 13$

On substituting the values of m and n, we get

$\rm :\longmapsto\:7( - 3) - 2( - 4) = - 13$

$\rm :\longmapsto\: - 21 + 8 = - 13$

$\rm :\longmapsto\: - 13 = - 13$

Hence, Verified

Now, Consider

$\red{\bf :\longmapsto\:3m - 4n}$

On substituting the values of m and n, we get

$\rm \:  =  \:  \: 3( - 3) - 4( - 4)$

$\rm \:  =  \:  \: - 9 + 16$

$\rm \:  =  \:  \: 7$

So,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \underbrace{\boxed{ \bf{ \: \: \: \: \: 3m - 4n = 7 \: \: \: \: \: }}}$