Question
Solve the following equations graphically $:\ 2+\frac{3 y}{x}=\frac{6}{x} , \frac{6 x}{y}-5=\frac{4}{y}$
✓
Answer
$2+\frac{3 y}{x}=\frac{6}{x}$
$\frac{6 x}{y}-5=\frac{4}{y}$
$2+\frac{3 y}{x}=\frac{6}{x}$
$ \Rightarrow 2 x+3 y=6 .....(1)$
$\frac{6 x}{y}-5=\frac{4}{y}$
$ \Rightarrow 6 x+5 y=4 ....(2)$
$2 x+3 y=6$
$\Rightarrow y=\frac{6-2 x}{3}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
Plotting points $(3, 0), (-3, 4), (0, 2)$ and joining them, we get a line $l_1$ which is the graph of equation $(1).$
$6x - 5y = 4$
$\Rightarrow y=\frac{6 x-4}{5}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
Plotting point $(1, 0.4), (2, 1.6), (3, 2.8)$ and joining them, we get a line $l_2$ which is the graph of equation $(2).$
The line $l_1$ and $l_2$ intersect at a unique point $\left(\frac{3}{2}, 1\right)$.
$\frac{6 x}{y}-5=\frac{4}{y}$
$2+\frac{3 y}{x}=\frac{6}{x}$
$ \Rightarrow 2 x+3 y=6 .....(1)$
$\frac{6 x}{y}-5=\frac{4}{y}$
$ \Rightarrow 6 x+5 y=4 ....(2)$
$2 x+3 y=6$
$\Rightarrow y=\frac{6-2 x}{3}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
| $x$ | $3$ | $-3$ | $0$ |
| $y$ | $0$ | $4$ | $2$ |
$6x - 5y = 4$
$\Rightarrow y=\frac{6 x-4}{5}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
| $x$ | $1$ | $2$ | $3$ |
| $y$ | $0.4$ | $1.6$ | $2.8$ |
The line $l_1$ and $l_2$ intersect at a unique point $\left(\frac{3}{2}, 1\right)$.
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