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# Show graphically that each of the following given systems of equations has infinitely many solutions: 2x+y=6,6x+3y=18.

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Solution

## Given equations are 2x + y = 6 and 6x + 3y = 18 Graph of 2x + y = 6: 2x + y = 6 ⇒y = −2x + 6 Putting x = 3, we get y = 0 Putting x = 1, we get y = 4 Putting x = 2, we get y = 2 Hence, the table is, X 3 1 2 Y 0 4 2 Plot the points A(3, 0), B(1, 4) and C(2, 2) on the graph paper. Join AC and BC to get the graph line of equation 2x + y = 6. Graph of 6x + 3y = 18: 6x + 3y = 18 ⇒ y=(−6x+18)3 Putting x = 0, we get y = -5 Putting x = 1, we get y = -2 Putting x = 2, we get y = 1 Hence, the table is: X 3 1 2 Y 0 4 2 These points are same as obtained above: Thus, we find that the two line graphs coincide. Hence, the given system of equations has infinitely many solutions  Suggest Corrections  1      Similar questions
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