Question

if 47 X + 31 y equal to 18 and 31 X + 47 y is equal to 60 then find value of x and y​

Answer 1

Answer:

1

Step-by-step explanation:

47x+31y=18 eq...1

31x+47y=60 eq...2

both are equation add

eq ....1+eq...2

x(47+31)+y(31+47)=18+60

78x+78y=78

78(x+y)=78

x+y=1

Answer 2

Answer

$\sf \dashrightarrow 47x + 32y = 18 \: \: --- (i)$

$\sf \dashrightarrow 31x + 47y = 60 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 47x + 32y = 18$

$\sf \dashrightarrow 47x = 18 - 32y$

$\sf \dashrightarrow x = \dfrac{18 - 31y}{47}$

Now, we should find the value of y by second equation.

$\sf \dashrightarrow 31x + 47y = 60$

$\sf \dashrightarrow 31 \bigg( \dfrac{18 - 31y}{47} \bigg) + 47y = 60$

$\sf \dashrightarrow \dfrac{558 - 961y}{47} + 47y = 60$

$\sf \dashrightarrow \dfrac{558 - 961y + 2209y}{47} = 60$

$\sf \dashrightarrow \dfrac{558 + 1248y}{47} = 60$

$\sf \dashrightarrow 558 + 1248y = 47 \times 60$

$\sf \dashrightarrow 558 + 1248y = 2820$

$\sf \dashrightarrow 1248y = 2820 - 558$

$\sf \dashrightarrow 1248y = 2262$

$\sf \dashrightarrow y = \dfrac{2262}{1248}$

$\sf \dashrightarrow y = \dfrac{1131}{624}$

Now, let's gind the valur of x by first equation.

$\sf \dashrightarrow 47x + 31y = 18$

$\sf \dashrightarrow 47x + 31 \bigg( \dfrac{1131}{625} \bigg) = 18$

$\sf \dashrightarrow 47x + \dfrac{35061}{625} = 18$

$\sf \dashrightarrow \dfrac{29375x + 35061}{625} = 18$

$\sf \dashrightarrow 29375x + 35061 = 625 \times 18$

$\sf \dashrightarrow 29375x + 35061 = 11250$

$\sf \dashrightarrow 29375x = 11250 - 35061$

$\sf \dashrightarrow 2937x = -23811$

$\sf \dashrightarrow x = \dfrac{-23811}{2937}$

$\sf \dashrightarrow x = \dfrac{-7937}{979}$

Hence, the values of x and y are $\sf \dfrac{-7937}{979}$ and $\sf \dfrac{1131}{624}$ respectively.