Solve for x and y: 2x-3 y =9, 3x+7 y =2 (y 0). - Vidyadip

Question

Solve for x and y:
$2\text{x}-\frac{3}{\text{y}}=\text{9},$
$\text{3x}+\frac{7}{\text{y}}=\text{2}$ $(\text{y}\neq0).$

✓

Answer

Putting $\frac{1}{\text{y}}=\text{v}$ the given equations become 2x - 3v = 9 ...(1) 3x + 7v = 2 ...(2)Multiplying (1) by 7 and (2) by 3, we get
14x - 21v = 63 ...(3)
9x + 21v = 6 ...(4)
Adding (3) and (4), we get
23x = 69
$\Rightarrow\text{x}=\frac{39}{13}=3$Putting x = 3 in (1), we get
2 × 3 - 3v = 9
-3v = 9 - 6
⇒ -3v = 3
⇒ v = -1
$\Rightarrow\frac{1}{\text{y}}=-1$⇒ y = -1
$\therefore$ The solution is x = 3 and y = 1

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