SOLUTION: 8x-6y=12 12x-9y=18 Solve and show check

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Question 1066683: 8x-6y=12
12x-9y=18
Solve and show check
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


8x-6y = 12   (1)

12x-9y = 18  (2)



Multiply equation (1) by 3/2:    (3/2)(8x-6y) = (3/2)(12)

                                     12x - 9y = 18



See how it matches equation (2).  This means the two equations are linearly dependent.   That means you really only have one equation with two unknowns (infinite number of solutions).  The solutions correspond to a line, and that line has equation  12x-9y = 18  or, in slope-intercept form:

 

                    -9y = 18 - 12x

                          highlight%28+y++=+%2812%2F9%29x+-+2+%29

                         

                            -2 is the y-axis intercept

                            12/9 is the slope

                       Here is a graph of the line:



+graph%28300%2C300%2C-10%2C10%2C+-10%2C10%2C+%2812%2F9%29x-2%29