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
$2 \times 3 - 3v = 9$
$-3v = 9 - 6$
$\Rightarrow -3v = 3$
$\Rightarrow v = -1$
$\Rightarrow\frac{1}{\text{y}}=-1$
$\Rightarrow y = -1$
$\therefore$ The solution is $x = 3$ and $y = 1$

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