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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