Question

96x-74y=64 ; 84x+52y=89 please solve​

Answer 1

Answer

$\sf \dashrightarrow 96x - 74y = 64 \: \: --- (i)$

$\sf \dashrightarrow 84x + 52y = 89 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 96x - 74y = 64$

$\sf \dashrightarrow 96x = 64 + 74y$

$\sf \dashrightarrow x = \dfrac{64 + 74y}{96}$

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

$\sf \dashrightarrow 84x + 52y = 89$

$\sf \dashrightarrow 84 \bigg( \dfrac{64 + 74y}{96} \bigg) + 52y = 89$

$\sf \dashrightarrow \dfrac{5376 + 6216y}{96} + 52y = 89$

$\sf \dashrightarrow \dfrac{5376 + 6216y + 4992y}{96} = 89$

$\sf \dashrightarrow \dfrac{5376 + 11208y}{96} = 89$

$\sf \dashrightarrow 5376 + 11208y = 89 \times 96$

$\sf \dashrightarrow 5376 + 11208y = 8544$

$\sf \dashrightarrow 11208y = 8544 - 5376$

$\sf \dashrightarrow 11208y = 3168$

$\sf \dashrightarrow y = \dfrac{3168}{11208}$

$\sf \dashrightarrow y = \dfrac{132}{467}$

Now, we can find the value of x by first equation.

$\sf \dashrightarrow 96x - 74y = 64$

$\sf \dashrightarrow 96x - 74 \bigg( \dfrac{132}{467} \bigg) = 64$

$\sf \dashrightarrow 96x - \dfrac{9768}{467} = 64$

$\sf \dashrightarrow \dfrac{44832x - 9768}{467} = 64$

$\sf \dashrightarrow 44832x - 9768 = 64 \times 467$

$\sf \dashrightarrow 44832x - 9768 = 29888$

$\sf \dashrightarrow 44832x = 29888 + 9768$

$\sf \dashrightarrow 44832x = 39656$

$\sf \dashrightarrow x = \dfrac{39656}{44832}$

$\sf \dashrightarrow x = \dfrac{4957}{5604}$

Hence, the values of x and y are $\sf \dfrac{4957}{5604}$ and $\sf \dfrac{132}{467}$ respectively.