Solve the following systems of equations graphically:

x + y = 6

x − y = 2

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#### Solution

The given equations are

x + y = 6 ...(1)

x − y = 2 ...(2)

Putting x = 0 in equation (1)we get

=> 0 + y = 6

=> y = 6

x = 0, y = 6

Putting y = 0 in equation (1) we get

=> x + 0 = 6

=> x = 6

Use the following table to draw the graph.

x | 0 | 6 |

y | 6 | 0 |

Draw the graph by plotting the two points A(0,6) and B(6,0) from the table

Graph of the equation ... (2)

x - y = 2 ..(2)

Putting x = 0 in equation (2) we get

=> 0 - y = 2

=> y = -2

x = 0, y = -2

Putting y = 0 in equation (2) we get

=> x - 0 = 2

=> x = 2

x = , y = 0

Use the following table to draw the graph.

x | 0 | 2 |

y | -2 | 0 |

Draw the graph by plotting the two points C(0,-2) and D(2,0) from table.

The two lines intersect at points P(4,2).

Hence x = 4, y = 2 is the solution.

Concept: Graphical Method of Solution of a Pair of Linear Equations

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