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does this system of equation have a solution?

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{x+3y=12

{1/3x+y=8

Oct 18th, 2017

x + 3y = 12

1/3x + y = 8

Solve for y second equation

1/3x + y = 8

y = 8 - 1/3x

Substitute (8-1/3x) for y in first equation

x + 3(8 - 1/3x) = 12

x + 27 - x = 12

27 = 12 not correct

No x solve the equation

x + 3y = 12, solve for y (first equation)

3y = 12 - x

y = 4 - 1/3x (first equation in slope intercept form)

y = 8 - 1/3x (second equation in slope intercept form)

Since both equations have the SAME SLOPE, THE LINES ARE PARALLEL AND THEREFORE DO NOT CROSS (INTERSECT), Therefore these equations have no solution (the x,y coordinates of these two equations would be where the two lines would intersect, but since they do not intersect, there is no solution).

Let me know if you have any other questions.


Apr 22nd, 2015

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