Question

Solve the following simultaneous equations 4m + 3n = 18; 3m - 2n = 5 ​

Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{m=3 \ and \ n=2 \ is \ the \ solution \ of}$

$\bold{the \ given \ simultaneous \ equations.}$

$\bold\orange{Given:}$

$\bold{=>4m+3n=18}$

$\bold{=>3m-2n=5}$

$\bold\pink{To \ find:}$

$\bold{Value \ of \ m \ and \ n.}$

$\bold\green{\underline{\underline{Solution}}}$

$\bold{The \ given \ simultaneous \ equations \ are:}$

$\bold{=>4m+3n=18...(1)}$

$\bold{=>3m-2n=5...(2)}$

$\bold{Multiply \ eq(1) \ by \ 2, \ we \ get}$

$\bold{=>8m+6n=36...(3)}$

$\bold{Multiply \ eq(2) \ by \ 3, \ we \ get}$

$\bold{=>9m-6n=15...(4)}$

$\bold{Add \ equations \ (3) \ and \ (4)}$

$\bold{=>8m+6n=36}$

$\bold{+}$

$\bold{=>9m-6n=15}$

_______________________

$\bold{17m=51}$

$\bold{m=\frac{51}{17}}$

$\bold{m=3}$

$\bold{Substituting \ m=3 \ in \ eq(1)}$

$\bold{4(3)+3n=18}$

$\bold{3n=18-12}$

$\bold{3n=6}$

$\bold{n=\frac{6}{3}}$

$\bold{n=2}$

$\bold\purple{\tt{\therefore{m=3 \ and \ n=2 \ is \ the \ solution \ of}}}$

$\bold\purple{\tt{the \ given \ simultaneous \ equations.}}$

Answer 2

$\large{\underline{\bf{\purple{Given:-}}}}$

✦ Two equations are given as :-

• 4m + 3n = 18
• 3m - 2n = 5

$\large{\underline{\bf{\purple{To\:Find:-}}}}$

✦ we need to find the value of m and n

$\huge{\underline{\bf{\red{Solution:-}}}}$

$\longmapsto \rm\:\:4m + 3n = 18...........(i)$

$\longmapsto \rm\:\3m - 2n = 5..........(ii)$

$\: \: \: \: \: \: \: \: \: \underbrace{ \pink{ \rm{By \: using \: elimination \: method \: }}}\:\:$

multiply equation (i) by 3 and equation (ii) by 4

we get,

$\longmapsto \rm\:(4m + 3n = 18) \times 3\: \\ \\\longmapsto \rm\:(3m - 2n = 5) \times 4 \\ \\ \longmapsto \rm\:we \: get : \\ \\\longmapsto \rm\:12m + 9n =5 4 .........(iii) \\ \\ \longmapsto \rm\:12m - 8n = 20.........(iv) \\ \\ \rm\:now \: solving \: eq. \: (iii) \: and \: (iv) \\ \\ \rm\:{ \cancel{12m}} + 9n = 54 \\\rm\:{ \cancel{12m}} - 8n = 20 \\ \: \: - \: \: \: \: \: \: \: \: \: + \: \: \: \: \: \: - \\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \rm\: \: \: \: \: \: \: \: \: \: \: \: \: \: 17n \: = 34 \\\rm\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: n \: = \cancel\frac{34}{17} \\ \bf\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: n = 2$

$\rm\:\:Now\: putting\: value\:of\:n \:in\:eq.\:(i)$

$\longmapsto \rm\:\:4m + 3n = 18 \\ \\\longmapsto \rm\:\:4m + 3 \times 2 = 18 \\ \\\longmapsto \rm\:\:4m + 6 = 18 \\ \\ \longmapsto \rm\:\:4m = 18 - 6 \\ \\ \longmapsto \rm\:\:4m = 12 \\ \\\longmapsto \rm\:\:m = \cancel\frac{12}{4} \\ \\\longmapsto \bf\:\:m = 3$

Hence,${\green {\bf{m = 3\:\:and\:\:\:n =2}}}\:\:$

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