Question

Describe the graphs of x + 3y = 6 and 2x + 6y = 12​

Answer 1

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Answer 2

Explanation:

x + 3y = 9

2x + 6y = 12

First you check if the two equations are compatible, that is

if they are parallel, they must not intersect.

Parallel means they have the same slope, given by dy/dx in general, and in the case of linear equations by the ratio of the y coefficient to that of x, that is 3 for the first equation, and 3 for the second. Since these two equations are parallel, they are multiple of each other. Now where these straight lines intersect the axis y = 0, that is the x-axis, is the constant term on the right hand side. Try it

Put y = 0 you get x = 9, for the first equation, and y = 0, x = 6 for the second equation, This is geometrically impossible, and therefore algebraically too. So this problem has no solution

Explanation:

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