##
**Solving
Simultaneous Equations Graphically**

While

**solving simultaneous equations graphically**, we find few pair of solutions for each of the two given equations in two separate tables. The pair of solutions of each equation are plotted in a graph and by joining them two separate straight lines are obtained. The coordinates of the point of intersection of two straight lines are the solution of the given simultaneous equations.**Steps for solving simultaneous equations graphically:**

i. Take first
equation, and equate it for one variable x or y in terms of other variable and
find some points (value of x and y) in a table.

ii. Take second
equation, and equate it for one variable x or y in terms of other variable and
find some points (value of x and y) in a table.

iii. Plot the points
of both equations in a graph and join the lines.

iv. Find the point
of intersection of two straight lines (value of x and y) which is the solution
of the given simultaneous equations.

This process of

**solving****simultaneous****equations graphically**will be clear by the following worked out examples.###
*Workout
Examples*

*Workout Examples*

*Example 1: Solve x + y = 7 and x – y = 3 by graphical method.*

*Solution:*

*Here,*

*x + y = 7 …………… (i)*

*x – y = 3 …………… (ii)*

*From equation (i),*

*x + y = 7*

*or, x = 7 – y*

x |
3 |
2 |

y |
4 |
5 |

*∴*

*Points are: (3, 4) and (2, 5)*

*From equation (ii),*

*x – y = 3*

*or, x = 3 + y*

x |
2 |
4 |

y |
-1 |
1 |

*∴*

*Points are: (3, 4) and (2, 5)*

*Now, plotting the points on graph,*

*From the above graph, point of intersection is (5, 2),*

*∴*

*x = 5*

*y = 2*

*Example 2: Solve 3x + y = 6 and x – 2y = 2 by graphical method.*

*Solution:*

*Here,*

*3x + y = 6 …………… (i)*

*x – 2y = 2 …………… (ii)*

*From equation (i),*

*3x + y = 6*

*or, y = 6 – 3x*

x |
1 |
2 |

y |
3 |
0 |

*∴*

*Points are: (1, 3) and (2, 0)*

*From equation (ii),*

*x – 2y = 2*

*or, x = 2 + 2y*

x |
4 |
6 |

y |
1 |
2 |

*∴*

*Points are: (4, 1) and (6, 2)*

*Now, plotting the points on graph,*

*From the above graph, point of intersection is (2, 0),*

*∴*

*x = 2*

*y = 0*

*Example 3: Solve 3x + 2y = 4 and 5x – y = 11*

*by graphical method.*

*Solution:*

*Here,*

*3x + 2y = 4 …………… (i)*

*5x – y = 11 …………… (ii)*

*From equation (i),*

*3x + 2y = 4*

*or, 3x = 4 – 2y*

*or, x = (4 – 2y)/3*

x |
0 |
2 |

y |
2 |
-1 |

*∴*

*Points are: (0, 2) and (2, -1)*

*From equation (ii),*

*5x – y = 11*

*or, 5x – 11 = y*

*or, y = 5x – 11*

x |
2 |
3 |

y |
-1 |
4 |

*∴*

*Points are: (2, -1) and (3, 4)*

*Now, plotting the points on graph,*

*From the graph, point of intersection is (2, -1),*

*∴*

*x = 2*

*y = -1*

*You can comment your questions or problems regarding the solving of simultaneous equations graphically here.*

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