# 3(y-2x) = 5(y-2x) - 8 -1/3(x-5y) = (y - x) - 4 solve for x,y

baxthum8 | High School Teacher | (Level 3) Associate Educator

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In order to solve: first use the distributive property on the first equation of: `3(y - 2x) = 5(y-2x)-8`  to get:

`3y - 6x = 5y - 10x - 8.`

and use the distributive property on 2nd equation to get:

`(-1/3)x + (5/3)y = y - x - 4`

Now simplify both equations to combine like terms into form:

`ax + by = c` .

`4x - 2y = -8`

`(-4/3)y + (8/3) x = -4` Next to make everything a little easier, multiply 2nd equation by 3 to get rid of denominators.  This will be:

`-4y + 8x = -12` and the other equation is:

`4x - 2y = -8` If we multiply the 2nd equation by -2, the x's will be opposites to combine the 2 equations together to isolate 1 variable like this:

`-2(4x - 2y = -8)` `rArr`           `-8x + 4y = 16`

and the other equation is:            `8x - 4y = -12`

by combining(adding) these together we get:  `0 = 4` ` `

Thus the solution would be: No solution, since `0!=4`

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