By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.
3x + y + 4 = 0, 6x-2y + 4 = 0
Given pair of equations is
3x + y + 4 = 0 …(i)
and 6x -2y + 4 = 0…(ii)
comparing with ax + by + c = 0
Here, a_{1} = , b_{1} = 1, c_{1} = 4;
And a_{2} = 6, b_{2} = - 2, c_{2} = 4;
a_{1} /a_{2} = 1/2
b_{1} /b_{2} = -3/6 = -1/2
c_{1} /c_{2} = 1
since a_{1}/a_{2} b_{1}/b_{2}
so system of equations is consistent with a unique solution.
We have,
When x = 0, then y = - 4
When x = - 1, then y = - 1
When x = - 2, then y = 2
0 | - 1 | - 2 | |
_{y} | - 4 | - 1 | 2 |
Points | B | C | A |
and
When x = 0, then y = 2
When x = - 1,then y = - 1
When x = 1,then y = 5
- 1 | 0 | 1 | |
_{y} | - 1 | 2 | 5 |
Points | C | Q | P |
Plotting the points B(0, - 4) and A( - 2,2),we get the straight tine AB. Plotting the points Q(0,2) and P(1,5) we get the straight line PQ. The lines AB and PQ intersect at C (-1, -1).