Question
Show graphically that the following system of equation is in-consistent (i.e. has no solution):
2y − x = 9
6y − 3x = 21
✓
Answer
The given equations are
2y − x = 9 ......(i)
6y − 3x = 21 .......(ii)
Putting x = 0 in equation (i), we get,
⇒ 2y - 0 = 9
$\Rightarrow\text{y}=\frac{9}{2}$
$\Rightarrow\text{x}=0,\ \text{y}=\frac{9}{2}$
Putting y = 0 in equation (i), we get,
⇒ 2 × 0 - x = 9
⇒ x = -9
⇒ x = -9, y = 0
Use the following table to draw the graph.
Draw the graph by plotting the two points $\text{A}\Big(0,\frac{9}{2}\Big),$ B(-9, 0) from table.
6y - 3x = 21 ......(ii)
Putting x = 0 in equation (ii), we get,
⇒ 6y - 3 × 0 = 21
$\Rightarrow\text{y}=\frac{7}{2}$
$\Rightarrow\text{x}=0,\ \text{y}=\frac{7}{2}$
Putting y = 0 in equation (ii), we get,
⇒ 6 × 0 - 3x = 21
⇒ x = -7
$\therefore$ x = -7, y = 0
Use the following table to draw the graph.
Draw the graph by plotting the two points $\text{C}\Big(0,\frac{7}{2}\Big),$ D(-7, 0) from table.
Here two lines are parallel and so don’t have common points. Hence the given system of equations has no solution.
2y − x = 9 ......(i)
6y − 3x = 21 .......(ii)
Putting x = 0 in equation (i), we get,
⇒ 2y - 0 = 9
$\Rightarrow\text{y}=\frac{9}{2}$
$\Rightarrow\text{x}=0,\ \text{y}=\frac{9}{2}$
Putting y = 0 in equation (i), we get,
⇒ 2 × 0 - x = 9
⇒ x = -9
⇒ x = -9, y = 0
Use the following table to draw the graph.
|
x
|
0
|
-9
|
|
y
|
$\frac{9}{2}$
|
0
|
6y - 3x = 21 ......(ii)
Putting x = 0 in equation (ii), we get,
⇒ 6y - 3 × 0 = 21
$\Rightarrow\text{y}=\frac{7}{2}$
$\Rightarrow\text{x}=0,\ \text{y}=\frac{7}{2}$
Putting y = 0 in equation (ii), we get,
⇒ 6 × 0 - 3x = 21
⇒ x = -7
$\therefore$ x = -7, y = 0
Use the following table to draw the graph.
| x | 0 | -7 |
| y | $\frac{7}{2}$ | 0 |
Here two lines are parallel and so don’t have common points. Hence the given system of equations has no solution.
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