Question

maths simultaneous equation of 4m+3n=63;3m-2n=5
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Answer 1

Here,

4m+3n=63......[1]

or

3m-2n=5.........[2]

now, [1] - [2]

4m+3n= 63

3m- 2n= 5

-__________________

m+5n= 58

》m=58- 5n.................[A]

now, [1]+[2]

4m+3n= 63

3m-2n= 5

+_______________

7m +n= 68

》n=68-7m

》n=68 -7(58- 5n)........{according to [A]}

》n=68-406+35n

》n-35n=-33

》-34n=-33

》n=-33/-34

》n= 0.97

now, according to [A]

m= 58- 5n

》m=58-5×0.97......(n=0.97)

》m=53.15

so, m=53.25

and n=0.97

Answer 2

$\large\underline{Given:-}$

• $\: \: \: \: \: {4m} \: + \: {3n} \: \: = \: \: {63}$
• $\: \: \: \: \: {3m} \: - \: {2n} \: \: = \: \: {5}$

$\large\underline{To find:-}$

• find the value of m and n.

$\large\underline{Solutions:-}$

• $\: \: \: \: \: {4m} \: + \: {3n} \: \: = \: \: {63} \: \: \: \: \: .....{(1)}.$
• $\: \: \: \: \: {3m} \: - \: {2n} \: \: = \: \: {5} \: \: \: \: \: .....{(2)}.$

»★ multiplying Eq. (1) by 2 and Eq. (2) by (3), we get.

$\: \: \: \: \: {8m} \: + \: {6n} \: \: = \: \: {126} \: \: \: \: \: .....{(3)}.$

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

»★ Subtracting Eq. (3) from Eq. (4).

${8m} \: + \: {6n} \: \: = \: \: {126} \\ {9m} \: - \: {6n} \: \: = \: \: {15} \\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:} \\ {17m} \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: {141}$

»★ Now, putting the value m in Eq. (1)

$\: \: \: \: \: \leadsto \: \: {4m} \: + \: {3n} \: \: = \: \: {63}$

$\: \: \: \: \: \leadsto \: \: {4} \: \times \frac{141}{17} \: + \: {3n} \: \: = \: \: {63}$

$\: \: \: \: \: \leadsto \: \: \frac{564}{17} \: + \: {3n} \: \: = \: \: {63}$

$\: \: \: \: \: \leadsto \: \: {564} \: + \: {3n} \: \: = \: \: {63} \: \times \: {17}$

$\: \: \: \: \: \leadsto \: \: {564} \: + \: {3n} \: \: = \: \: {1071}$

$\: \: \: \: \: \leadsto \: \: {3n} \: \: = \: \: {1071} \: - \: {564}$

$\: \: \: \: \: \leadsto \: \: {3n} \: \: = \: \: {507}$

$\: \: \: \: \: \leadsto \: \: {n} \: \: = \: \: \frac{507}{3}$

$\: \: \: \: \: \leadsto \: \: {n} \: \: = \: \: {169}$

»★ Hence,

$\: \: \: \: \: The \: \: value \: \: of \: \: m \: \: and \: \: n \: \: is \: \: \frac{141}{17} \: \: and \: \: {169}.$

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