Question
Show graphically that the following system of equation is in-consistent (i.e. has no solution):
$x - 2y = 6$
$3x - 6y = 0$
✓
Answer
The given equations are,
$x - 2y = 6 .......(i)$
$3x - 6y = 0 ........(ii)$
From (i), $\text{y}=\frac{\text{x}-6}{2}\ ......(\text{iii})$
Putting $x = 0$ in $(iii),$ we get $y = -3$
Putting $x = 2$ in $(iii),$ we get $y = -2$
Putting $x = 4$ in $(iii)$, we get $y = -1$
From (ii), $\text{y}=\frac{3\text{x}}{6}\ ......(\text{iv})$
Putting $x = 0$ in $(iv),$ we get $y = 0$
Putting $x = 2$ in $(iii),$ we get $y = 1$
Putting $x = 4$ in $(iii),$ we get $y = 2$
When we plot these points on graph paper we observe that both linesare parallel to each other means they have no solution so they are in-consistent.
$x - 2y = 6 .......(i)$
$3x - 6y = 0 ........(ii)$
From (i), $\text{y}=\frac{\text{x}-6}{2}\ ......(\text{iii})$
Putting $x = 0$ in $(iii),$ we get $y = -3$
Putting $x = 2$ in $(iii),$ we get $y = -2$
Putting $x = 4$ in $(iii)$, we get $y = -1$
|
$x$
|
$0$
|
$2$
|
$4$
|
|
$y$
|
$-3$
|
$-2$
|
$-1$
|
Putting $x = 0$ in $(iv),$ we get $y = 0$
Putting $x = 2$ in $(iii),$ we get $y = 1$
Putting $x = 4$ in $(iii),$ we get $y = 2$
|
$x$
|
$0$
|
$2$
|
$4$
|
|
$y$
|
$0$
|
$1$
|
$2$
|
When we plot these points on graph paper we observe that both linesare parallel to each other means they have no solution so they are in-consistent.
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