Question

Solve it by using Substitution method
$\frac{3x}{2} - \frac{5y}{3} = - 2$
$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$
Give quality ans.
Otherwise ans reported as well as I'd.
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Answer 1

Answer:

$\mathtt\pink{SOLUTION:-}$

$\mathtt\purple{\frac{3x}{2} - \frac{5y}{3} = - 2}$

$\mathtt\purple{\frac{x}{3} + \frac{y}{2} = \frac{13}{6}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt\pink{FROM \: EQUATION \: 1}$

$\mathtt\purple{\frac{3x}{2} - \frac{5y}{3} = - 2}$

$\mathtt\purple{\frac{9x-10y}{6} = - 2}$

$\mathtt\purple{9x-10y = - 12 --Eq(iii)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt\pink{FROM \: EQUATION \: 2}$

$\mathtt\purple{\frac{x}{3} + \frac{y}{2} = \frac{13}{6}}$

$\mathtt\purple{\frac{2x+3y}{6}= \frac{13}{6}}$

$\mathtt\purple{2x+3y= 13 ----Eq(iv)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt\pink{FROM \: EQUATION \: 4}$

$\mathtt\purple{2x+3y = 13}$

$\mathtt\purple{2x=13-3y}$

$\mathtt\purple{x=\frac{13-3y}{2}-----Eq(v)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt\pink{IN \: EQUATION \: 3}$

$\mathtt \purple{9( \frac{13 - 3y}{2}) - 10y = - 12 }$

$\mathtt\purple{ \frac{117 - 27y}{2} - \frac{20}{y} = - 12}$

$\mathtt\purple{117 - 47y = - 24}$

$\mathtt\purple{ - 47y = - 24 - 117}$

$\mathtt\purple{ - 47y = - 141}$

$\mathtt \purple{y = \frac{141}{47} }$

$\mathtt\purple{y = 3}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt\pink{IN \: EQUATION \: 5}$

$\mathtt\purple{x = \frac{13 - 3 \times 3}{2} }$

$\mathtt\purple{x = \frac{13 - 9}{2} }$

$\mathtt\purple{x = \frac{4}{2} }$

$\mathtt\purple{x = 2}$

Answer 2

$\begin{gathered} \frac{3x}{2} - \frac{5y}{3} = - 2 \\ \\ \bf multiplying \: the \: {eq}^{n} \: by \: 6 \\ \\ 6( \frac{3x}{2} - \frac{5y}{3} = - 2) \\ \\ \frac{18x}{2} - \frac{30y}{3} = - 12 \\ \\ 9x - 10y = - 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(1)\end{gathered}$

$\begin{gathered} \frac{x}{3} + \frac{y}{2} = \frac{13}{6} \\ \\ \bf multiplying \: the \: {eq}^{n} \: by \: 6 \\ \\ 6( \frac{x}{3} + \frac{y}{2} = \frac{13}{6} ) \\ \\ \frac{6x}{3} + \frac{6y}{2} = 13 \\ \\ 2x + 3y = 13 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(2)\end{gathered}$

From equation 1 :

$\begin{gathered}9x = - 12 + 10y \\ \\ \bf x = \frac{ - 12 + 10y}{9} \end{gathered}$

$\begin{gathered}2( \frac{ - 12 + 10y}{9} ) + 3y = 13 \\ \\ \frac{ - 24 + 20y}{9} + 3y = 13 \\ \\ \frac{ - 24 + 20y + 27y}{9} = 13 \\ \\ - 24 + 47y = 13 \times 9 \\ \\ - 24 + 47y = 117 \\ \\ 47y = 117 + 24 \\ \\ y = \frac{141}{47} \\ \\ \bf y = 3\end{gathered}$

$\begin{gathered}2x + 3(3) = 13 \\ \\ x + 9 = 13 \\ \\ x = 13 - 9 \\ \\ \bf x = 4\end{gathered}$

Hope it helps! ;))