Question
Solve the following equations graphically $:\ 2x + 4y = 7;3x + 8y = 10$
✓
Answer
$ 2 x+4 y=7$
$3 x+8 y=10$
$2 x+4 y=7 ....(1)$
$3 x+8 y=10 ....(2) $
Now$, 2 x+4 y=7$
$ \Rightarrow 4 y=7-2 x$
$\Rightarrow y=\frac{7-2 x}{4} $
Corresponding values of $x$ and $y$ can be tabulated as $:$
Plotting points $(2, 0.75), (3, 0.25), (3, 0.25), (4, -0.25)$ and joining them$,$ we get a line $l_1$ which is the graph of equation $(1).$
Again$, 3x + 8y = 10$
$\Rightarrow x=\frac{10-8 y}{3}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
Plotting points $(6, 1), (2, 2), (0, 1.25)$ and joining them$,$ we get a line $l_2$ which is the graph of equation $(2).$
The two lines $l_1$ and $l_2$ intersect at the point $(4, -0.25),$
i.e., $\left(4,-\frac{1}{4}\right)$..
Hence $x = 4$ and $y = \frac{-1}{4}$ is the unique solution of the given equations.
$3 x+8 y=10$
$2 x+4 y=7 ....(1)$
$3 x+8 y=10 ....(2) $
Now$, 2 x+4 y=7$
$ \Rightarrow 4 y=7-2 x$
$\Rightarrow y=\frac{7-2 x}{4} $
Corresponding values of $x$ and $y$ can be tabulated as $:$
| $x$ | $2$ | $3$ | $4$ |
| $y$ | $0.75$ | $0.25$ | $-0.25$ |
Again$, 3x + 8y = 10$
$\Rightarrow x=\frac{10-8 y}{3}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
| $x$ | $6$ | $-2$ | $0$ |
| $y$ | $-1$ | $2$ | $1.25$ |
The two lines $l_1$ and $l_2$ intersect at the point $(4, -0.25),$
i.e., $\left(4,-\frac{1}{4}\right)$..
Hence $x = 4$ and $y = \frac{-1}{4}$ is the unique solution of the given equations.
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