The reason for the equations x-2 y-5 and 4 x-8 y-20 to have infinite solutions isA- The graph of the system of equations meets at infinityB- The graph reaches infinityC- The graph of both the equations is the same lineD- none of these

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The reason fo...

Question

The reason for the equations $x + 2 y = 5$ and $4 x + 8 y = 20$ to have infinite solutions is

The graph of the system of equations meets at infinity

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The graph reaches infinity

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The graph of both the equations is the same line

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none of these

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Solution

The correct option is C
The graph of both the equations is the same line

Both equations represent the same line.

In the line $4 x + 8 y = 20$ , if we take the common factor 4 out , we get $x + 2 y = 5$ which is same as the other line.

So these lines are coincident and therefore have infinite points of intersections(solutions)

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The reason for the equations x+2y=5 and 4x+8y=20 to have infinite solutions is

The reason for the equations $x + 2 y = 5$ and $4 x + 8 y = 20$ to have infinite solutions is