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, a_{1} = 1, b_{1} = 1, c_{1} = - 3;

And a_{2} = 3, b_{2} = 3, c_{2} = - 9;

a_{1} /a_{2} = 1/3

b_{1} /b_{2} = 1/3

c_{1} /c_{2} = 1/3

Here, a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}, 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 |

| 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 |

| 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.

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