Question

Math simultaneous equations of
4m + 2n= 6: m+4m = 18​

Answer 1

$\large\underline{Given:-}$

• $\: \: \: \: \: {4m} \: + \: {2n} \: \: = \: \: {6}$
• $\: \: \: \: \: {m} \: + \: {4n} \: \: = \: \: {18}$

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

• find the value of m and n.

$\large\underline{Solutions:-}$

• $\: \: \: \: \: {4m} \: + \: {2n} \: \: = \: \: {6} \: \: \: \: \: .....{(1)}.$
• $\: \: \: \: \: {m} \: + \: {4n} \: \: = \: \: {18} \: \: \: \: \: .....{(2)}.$

»★ multiplying Eq. (1) by 1 and Eq. (2) by 4 , we get.

• $\: \: \: \: \: {4m} \: + \: {2n} \: \: = \: \: {6} \: \: \: \: \: .....{(3)}.$
• $\: \: \: \: \: {4m} \: + \: {16n} \: \: = \: \: {72} \: \: \: \: \: .....{(4)}.$

»★ Subtracting Eq. (3) from Eq. (4).

${4m} \: + \: {2n} \: \: = \: \: {6} \\ {4m} \: + \: {16n} \: \: = \: \: {72} \\ \underline{- \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: = \: \: \: \: - \: \: \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: \: \: \: {14n} \: \: \: = \: \: \: {66}$

$\: \: \: \: \: \leadsto \: \: {n} \: \: = \: \: \frac{66}{14}$

$\: \: \: \: \: \leadsto \: \: {n} \: \: = \: \: \frac{33}{7}$

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

$\: \: \: \: \: \leadsto \: \: {4m} \: + \: {2n} \: \: = \: \: {6}$

$\: \: \: \: \: \leadsto \: \: {4} \: + \: {2} \: \times \: \frac{33}{7} \: \: = \: \: {6}$

$\: \: \: \: \: \leadsto \: \: {4} \: + \: \frac{66}{7} \: \: = \: \: {6}$

$\: \: \: \: \: \leadsto \: \: {4m} \: + \: {66} \: \: = \: \: {6} \: \times \: {7}$

$\: \: \: \: \: \leadsto \: \: {4m} \: + \: {66} \: \: = \: \: {42}$

$\: \: \: \: \: \leadsto \: \: {4m} \: \: = \: \: {42} \: - \: {66}$

$\: \: \: \: \: \leadsto \: \: {4m} \: \: = \: \: {-24}$

$\: \: \: \: \: \leadsto \: \: {m} \: \: = \: \: \frac{-24}{4}$

$\: \: \: \: \: \leadsto \: \: {m} \: \: = \: \: {-6}$

»★ Hence,

$\: \: \: \: \: The \: \: value \: \: of \: \: m \: \: and \: \: n \: \: is \: \: {-6} \: \: and \: \: \frac{33}{7}.$

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Answer 2

Answer:

here is your answer ⏩

4m +2n=6--(1)

m+4n =18--(2)

(2)×4=>

4m +16n=72-(3)

now, (3)-(1)

14n=66

n=33/7

again, (1)=>

4m+2×33/7=6

4m=6-66/7

m= -6/7

hope it helps you siso✨✨