Solve: 2x-3/y=9 and 3x+7/y=2
Elimination Method
2x-$\frac{3}{y}$=9 —-(i)
3x+$\frac{7}{y}$=2—-(ii)
Multiplying Equation (i) by 7 and Equation (ii) by 3 we get,
14x – $\frac{21}{y}$ = 63 —(iii)
9x + $\frac{21}{y}$ = 6 —-(iv)
Adding Equations (iii) and (iv) we get,
14x – $\frac{21}{y}$+9x + $\frac{21}{y}$ =63+6
⇒ 23x = 69
⇒ x= $\frac{69}{23}$
⇒ x = 3
Substituting the value of x in equation (i) we get,
2(3) – $\frac{3}{y}$ = 9
⇒ 6 -$\frac{3}{y}$=9
⇒ 6-9=$\frac{3}{y}$
⇒ -3=$\frac{3}{y}$
⇒ -3y=3
⇒ y= $\frac{3}{ – 3}$
⇒ y=-1
∴ Required Solutions are x = 3 , y=-1 [Ans]
Substitution Method
2x-$\frac{3}{y}$=9 —-(i)
3x+$\frac{7}{y}$=2—-(ii)
From Equation (i) we get,
2x-$\frac{3}{y}$=9
⇒ 2x = $\frac{3}{y}$ +9
⇒ 2x=$\frac{3 + 9y}{y}$
⇒ x = $\frac{3 + 9y}{2y}$ —-(iii)
Substituting the value of x in equation (ii) we get,
3x+$\frac{7}{y}$=2
$3\left(\frac{3 + 9y}{2y}\right) + \frac{7}{y} = 2$
$\Rightarrow \frac{9 + 27y}{2y} + \frac{7}{y} = 2$
$\Rightarrow \frac{9 + 27y + 14}{2y} = 2$
$\Rightarrow 23 + 27y = 4y$
$\Rightarrow 23 = 4y – 27y$
$\Rightarrow 23 = – 23y$
$\Rightarrow y = \frac{23}{ – 23}$
$\Rightarrow y = – 1$
From equation (iii) we get,
${\mathrm{x}} = \frac{3 + 9{\mathrm{y}}}{2{\mathrm{y}}}$
$\Rightarrow {\mathrm{x}} = \frac{3 + 9( – 1)}{2( – 1)}$
$\Rightarrow {\mathrm{x}} = \frac{3 – 9}{ – 2}$
$\Rightarrow {\mathrm{x}} = \frac{ – 6}{ – 2}$
$\Rightarrow {\mathrm{x}} = 3$
∴ Required Solutions are x = 3 , y=-1 [Ans]