Question
Solve the following equations graphically $:\ x+ 2y - 7 = 0;2x - y - 4 = 0$
✓
Answer
$x+ 2y - 7 = 0........(1)$
$2x - y - 4 = 0.......(2)$
$x+ 2y - 7 = 0$
$\Rightarrow x = 7 - 2y$
Corresponding values of $x$ and $y$ can be tabulated as :
Plotting points $(7, 0), (3, 2), (1, 3)$ and joining them, we get a line $l_1$ which is the graph of equation $(1).$
$2x - y - 4$
$\Rightarrow y = 2x - 4$
Corresponding values of $x$ and $y$ can be tabulated as $:$
Plotting points $(0, -4), (3, 2), (2, 0)$ and joining them, we get a line $l_2$ which is the graph of equation $(2).$
The lines $l_1$ and $l_2$ intersect at a unique point $(3, 2).$
$2x - y - 4 = 0.......(2)$
$x+ 2y - 7 = 0$
$\Rightarrow x = 7 - 2y$
Corresponding values of $x$ and $y$ can be tabulated as :
| $x$ | $7$ | $3$ | $1$ |
| $y$ | $0$ | $2$ | $3$ |
$2x - y - 4$
$\Rightarrow y = 2x - 4$
Corresponding values of $x$ and $y$ can be tabulated as $:$
| $x$ | $0$ | $3$ | $2$ |
| $y$ | $-4$ | $2$ | $0$ |
The lines $l_1$ and $l_2$ intersect at a unique point $(3, 2).$
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