Question

slove: X/7+y/3=5;x/5-y/9=1

Answer 1

the answer of this question.

Answer 2

Answer

$\sf \dashrightarrow \dfrac{x}{7} + \dfrac{y}{3} = 5 \: \: --- (i)$

$\sf \dashrightarrow \dfrac{x}{5} - \dfrac{y}{9} = 1 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow \dfrac{3x + 7y}{21} = 5$

$\sf \dashrightarrow 3x + 7y = 21 \times 5$

$\sf \dashrightarrow 3x + 7y = 105 \: \: --- (iii)$

By second equation,

$\sf \dashrightarrow \dfrac{x}{5} - \dfrac{y}{9} = 1$

$\sf \dashrightarrow \dfrac{9x - 5y}{45} = 1$

$\sf \dashrightarrow 9x - 5y = 45 \: \: --- (iv)$

By third equation,

$\sf \dashrightarrow 3x + 7y = 105$

$\sf \dashrightarrow 3x = 105 - 7y$

$\sf \dashrightarrow x = \dfrac{105 - 7y}{3}$

Now, let's find the value of y by fourth equation.

$\sf \dashrightarrow 9x - 5y = 45$

$\sf \dashrightarrow 9 \bigg( \dfrac{105 - 7y}{3} \bigg) - 5y = 45$

$\sf \dashrightarrow \dfrac{945 - 63y}{3} - 5y = 45$

$\sf \dashrightarrow \dfrac{945 - 64y - 15y}{3} = 45$

$\sf \dashrightarrow \dfrac{945 - 79y}{3} = 45$

$\sf \dashrightarrow 945 - 79y = 45 \times 3$

$\sf \dashrightarrow 945 - 79y = 135$

$\sf \dashrightarrow -79y = 135 -945$

$\sf \dashrightarrow -79y = -810$

$\sf \dashrightarrow y = \dfrac{-810}{-79}$

$\sf \dashrightarrow y = \dfrac{810}{79}$

Now, let's find the value of x by third equation.

$\sf \dashrightarrow 3x + 7y = 105$

$\sf \dashrightarrow 3x + 7 \bigg( \dfrac{810}{79} \bigg) = 105$

$\sf \dashrightarrow 3x + \dfrac{5670}{79} = 105$

$\sf \dashrightarrow \dfrac{237x + 5670}{79} = 105$

$\sf \dashrightarrow 237x + 5670 = 105 \times 79$

$\sf \dashrightarrow 237x + 5670 = 8295$

$\sf \dashrightarrow 237x = 8295 - 5670$

$\sf \dashrightarrow 237x = 2625$

$\sf \dashrightarrow x = \dfrac{2625}{237}$

$\sf \dashrightarrow x = \dfrac{875}{79}$

Hence, the values of x and y are 875/79 and 810/79 respectively.