**Solution:**

(I) Given

x + y = 3 …. (i)

(i) Put value x=3 in equation (i)

We get, y = 3 – 3

⇒ y = 0

ii. Put value y = 5 in equation (i)

We get, x = 3 – 5

⇒ x = -2

iii. Put value y = 3 in equation (i)

We get, x = 3 – 3

⇒ x = 0

Now the table becomes,

x | 3 | -2 | 0 |

y | 0 | 5 | 3 |

(x, y) | (3, 0) | (-2, 5) | (0, 3) |

(2) Given

x – y = 4 ……. (ii)

i. Put value y = 0 in equation (ii)

we get, x = 4 – 0

⇒ x = 4

ii. Put value x = –1 in equation (ii)

we get, – y = 5

iii. Put value y = –4 in equation (ii)

we get, x = 4 + 4

⇒ x = 8

x | 4 | -1 | 0 |

y | 0 | -5 | -4 |

(x, y) | (4, 0) | (-1, -5) | (0, -4) |

**(2) x + y = 5; x – y = 3**

**Solution:**

x + y = 5 …. (i)

x | 0 | 2 | 4 |

y | 5 | 3 | 1 |

(x, y) | (0, 5) | (2, 3) | (4, 1) |

x – y = 3 …… (ii)

x | 0 | 2 | 4 |

y | -3 | -1 | 1 |

(x, y) | (0, -3) | (2, -1) | (4, 1) |

Calculating intersecting point

x + y = 5

x – y = 3

which implies

2x = 8

x = 8/2

x = 4

Putting x= 4 in equation (i)

4 + y = 5

y = 5 – 4

y = 1

Intersection Point (4,1)

**(3) x + y = 0; 2x – y = 9**

**Solution:**

x + y = 0 …. (i)

x | 1 | 3 | 5 |

y | -1 | -3 | -5 |

(x, y) | (1, -1) | (3, -3) | (5, -5) |

2x – y = 9 …. (ii)

x | 2 | 3 | 4 |

y | -5 | -3 | -1 |

(x, y) | (2, -5) | (3, -3) | (4, -1) |

Calculating intersecting point

x + y = 0

2x – y = 9

3x = 9

x = 9/3

x = 3

Putting x= 3 in equation (i)

3 + y = 0

y = 0 – 3

y = -3

Intersection point (3, –3)

**(4) 3x – y = 2; 2x – y = 3**

**Solution:**

3x – y = 2 …… (i)

x | 0 | 1 | -1 |

Y | -2 | 1 | -5 |

(x, y) | (0, -2) | (1, 1) | (-1, -5) |

2x – y = 3 …… (ii)

x | 3 | 2 | -1 |

y | 3 | 1 | -5 |

(x, y) | (3, 3) | (2, 1) | (-1, -5) |

Calculating intersecting point

3x – y = 2

– 2x + y = -3

x = -1

Putting x= –1 in equation (i)

3× –1 – y = 2

– 3 – y = 2

– y = 2 + 3

y = -5

Intersection point (–1, –5)

**(5) 3x – 4y = –7; 5x – 2y = 0**

**Solution:**

3x – 4y = 7 …. (i)

When x = 0, 4y = 7, y = 7/4

When y = 0, 3x = -7, x = -7/3

5x – 2y = 0 …… (ii)

When x = 0, y = 0

When x = 1, y = 5/2

Plotting both the graphs we get,

Calculating intersecting point

3x – 4y = -7

5x – 2y = 0

x = -1

Putting x= –1 in equation (i)

3 × –1 – y = 2

– 3 – y = 2

– y = 2 + 3

y = – 5

Intersection point (–1, –5)