Question
Solve the following equations graphically$:\ x-2 y=2 , \frac{x}{2}-y=1$
✓
Answer
$x-2 y=2$
$\frac{x}{2}-y=1$
$x-2 y=2 ....(1)$
$\frac{x}{2}-y=1 ....(2)$
$x-2 y=2$
$\Rightarrow x=2+2 y$
Corresponding values of $x$ and $y$ can be tabulated as$ :$
Again $\frac{x}{2}-y=1$
$\Rightarrow y =\frac{x}{2}-1$
Corresponding values of $x$ and $y$ can be tabulated as $:$
Plotting points $(0, -1), (2, 0), (4, 1)$ and joining them$,$ we get a line $l_1$ which is the graph for both the equation $(1)$ and $(2).$
Hence$,$ the given system of equations has infinitely many solutions.
$\frac{x}{2}-y=1$
$x-2 y=2 ....(1)$
$\frac{x}{2}-y=1 ....(2)$
$x-2 y=2$
$\Rightarrow x=2+2 y$
Corresponding values of $x$ and $y$ can be tabulated as$ :$
| $x$ | $2$ | $0$ | $4$ |
| $y$ | $0$ | $-1$ | $1$ |
$\Rightarrow y =\frac{x}{2}-1$
Corresponding values of $x$ and $y$ can be tabulated as $:$
| $x$ | $0$ | $2$ | $4$ |
| $y$ | $-1$ | $0$ | $1$ |
Hence$,$ the given system of equations has infinitely many solutions.
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