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