Question
Solve the following equations graphically $\ :x + 3y = 8 , 3x = 2 + 2y$
✓
Answer
$ x+3 y=8$
$3 x=2+2 y$
$x+3 y=8 .....(1)$
$3 x=2+2 y .....(2) $
Now$, x+3 y=8$
$ \Rightarrow y=\frac{8-x}{3}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
Plotting points $(-1,3),(2,2),(5,1)$ and joiniing them$,$ we get a line I$,$ which is the graph of equation $(1).$
Again$, 3 x =2+2 y$
$\Rightarrow x =\frac{2 x+2 y}{3}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
Plotting points $(2, 2), (4, 5), (0, -1)$ and joining them$,$ we get a line $I_2$ which is the graph of equation $(2).$
The two lines $I_2$ and $I_2$ intersect at the point $(2, 2).$
Hence$, x = 2, y = 2$ is the unique solution of the given equation.
$3 x=2+2 y$
$x+3 y=8 .....(1)$
$3 x=2+2 y .....(2) $
Now$, x+3 y=8$
$ \Rightarrow y=\frac{8-x}{3}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
| $x$ | $-1$ | $2$ | $5$ |
| $y$ | $3$ | $2$ | $1$ |
Again$, 3 x =2+2 y$
$\Rightarrow x =\frac{2 x+2 y}{3}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
| $x$ | $2$ | $4$ | $0$ |
| $y$ | $2$ | $5$ | $-1$ |
The two lines $I_2$ and $I_2$ intersect at the point $(2, 2).$
Hence$, x = 2, y = 2$ is the unique solution of the given equation.
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