Question
Solve the following equations graphically $:\ x + 4y + 9 = 0 , 3y = 5x - 1$
✓
Answer
$x+4 y+9=0$
$3 y=5 x-1$
$x+4 y+9 .....(1)$
$3 y=5 x-1 .....(2)$
Now, $x+4 y=-9$
$\Rightarrow x=-9-4 y$
Corresponding values of $x$ and $y$ can be tabulated as $:$
Plotting points $(4, -3), (-1, -2)$ and $(-5, -1)$ and joining them, we geta line $l_1$ which is the graph of equation $(!).$
Again$, 3y = 5 x -1$
$\Rightarrow y=\frac{5 x-1}{3}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
Plotting points $(-4, -7), (-1, -2), (5, 8)$ and joining them we get a line $l_2$ which is the graph of equation $(2).$
The two line $l_1$ and $l_2$ intersect at a unique point $(-1, -2)$.
Thus$, x = -1$ and $y = -2$ is the unique solution of the given equations.
$3 y=5 x-1$
$x+4 y+9 .....(1)$
$3 y=5 x-1 .....(2)$
Now, $x+4 y=-9$
$\Rightarrow x=-9-4 y$
Corresponding values of $x$ and $y$ can be tabulated as $:$
| $x$ | $4$ | $-1$ | $-5$ |
| $y$ | $-3$ | $-2$ | $-1$ |
Again$, 3y = 5 x -1$
$\Rightarrow y=\frac{5 x-1}{3}$
Corresponding values of $x$ and $y$ can be tabulated as $:$
| $x$ | $-4$ | $-1$ | $5$ |
| $y$ | $-7$ | $-2$ | $8$ |
The two line $l_1$ and $l_2$ intersect at a unique point $(-1, -2)$.
Thus$, x = -1$ and $y = -2$ is the unique solution of the given equations.
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