Question
Solve for x and y:
$\text{x}+\frac{5}{\text{y}}=\text{6},$
$\text{3x}-\frac{8}{\text{y}}=\text{5}\ (\text{y}\neq0).$
$\text{x}+\frac{5}{\text{y}}=\text{6},$
$\text{3x}-\frac{8}{\text{y}}=\text{5}\ (\text{y}\neq0).$
✓
Answer
The given equations are $\text{x}+\frac{6}{\text{y}}=6$ and $\text{3x}-\frac{8}{\text{y}}=5$ Putting $\frac{1}{\text{y}}=\text{x}$ the given equations become x + 6v = 6 ...(1) 3x - 8v = 5 ...(2)Multiplying (1) by 4 and (2) by 3, we get
4x + 24v = 24 ...(3)
9x - 24v = 15 ...(4)
Adding (3) and (4), we get
13x = 24 + 15 = 39
$\therefore\text{x}=\frac{39}{13}=3$Putting x = 3 in (1), we get
$3+\text{6v}=6$ $\therefore\text{6v}=6-3=3$ $\text{v}=\frac{3}{6}=\frac{1}{2}$ $\text{v}=\frac{1}2{}$ $\Rightarrow\frac{1}{\text{y}}=\frac{1}{2}$ $\Rightarrow\text{y}=2$$\therefore$ The solution is x = 3 and y = 2
4x + 24v = 24 ...(3)
9x - 24v = 15 ...(4)
Adding (3) and (4), we get
13x = 24 + 15 = 39
$\therefore\text{x}=\frac{39}{13}=3$Putting x = 3 in (1), we get
$3+\text{6v}=6$ $\therefore\text{6v}=6-3=3$ $\text{v}=\frac{3}{6}=\frac{1}{2}$ $\text{v}=\frac{1}2{}$ $\Rightarrow\frac{1}{\text{y}}=\frac{1}{2}$ $\Rightarrow\text{y}=2$$\therefore$ The solution is x = 3 and y = 2
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