Question
Solve the following equations graphically $:\ 2x - 6y + 10 = 0 , 3x - 9y + 25 = 0$
✓
Answer
$2 x-6 y+10=0$
$3 x-9 y+25=0$
$2 x-6 y+10=0 ....(1)$
$3 x-9 y+25=0 ....(1)$
$2 x-6 y+10=0$
$\Rightarrow x=\frac{6 y-10}{2}$
$=3 y-5$
Corresponding values of $x$ and $y$ can be tabulated as :
Plotting points $(-5, 0),(-2, 1), (1, 2)$ and joining them$,$ we get a line $l_1$ which is the graph of the equation $(1).$
Again$, 3x - 9y + 25 = 0$
$\Rightarrow x =\frac{9 y-25}{3}$
Corresponding values of $x$ and $y$ can be tabulated as :
Plotting points $\left(0, \frac{25}{9}\right),\left(\frac{-25}{3}, 0\right)$ and joining them$,$ we get a line $I _2$ which is the graph of the equation $(2).$
The line $l_1$ and $l_2$ do not intersect each other.
Thus$,$ the given equations do not have any solution.
$3 x-9 y+25=0$
$2 x-6 y+10=0 ....(1)$
$3 x-9 y+25=0 ....(1)$
$2 x-6 y+10=0$
$\Rightarrow x=\frac{6 y-10}{2}$
$=3 y-5$
Corresponding values of $x$ and $y$ can be tabulated as :
| $x$ | $-5$ | $-2$ | $1$ |
| $y$ | $0$ | $1$ | $2$ |
Again$, 3x - 9y + 25 = 0$
$\Rightarrow x =\frac{9 y-25}{3}$
Corresponding values of $x$ and $y$ can be tabulated as :
| $x$ | $0$ | $\frac{-25}{3}=8.33$ |
| $y$ | $\frac{25}{9}=2.77$ | $ 0$ |
The line $l_1$ and $l_2$ do not intersect each other.
Thus$,$ the given equations do not have any solution.
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