By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.
x + y = 3, 3x + 3y = 9
Given pair of equations is
x + y = 3 …(i)
and 3x + 3y = 9 …(ii)
On comparing with ax + by + c = 0
Here, a1 = 1, b1 = 1, c1 = - 3;
And a2 = 3, b2 = 3, c2 = - 9;
a1 /a2 = 1/3
b1 /b2 = 1/3
c1 /c2 = 1/3
Here, a1/a2 = b1/b2 = c1/c2, i.e. coincident lines
Hence, the given pair of linear equations is coincident and having infinitely many solutions.
The given pair of linear equations is consistent.
Now, 
If x = 0 then y = 3, If x = 3, then y = 0.
x | 0 | 3 |
y | 3 | 0 |
Points | A | B |
and 
If x = 0 then y = 3, if x = 1, then y = 2, and if x = 3, then y = 0.
x | 0 | 1 | 3 |
y | 3 | 2 | 0 |
Points | C | D | E |
Plotting the points A(0, 3) and B(3, 0), we get the line AB. Again, plotting the points C(0, 3) and D(1, 2) and E(3, 0), we get the line CDE.