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{{:(-13=ay+24x),(9+6bx=5y):} If the system of equations above has no solutions, and a and b are constants, then what is the value of |a+b| ?

Answer»

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Solution :REARRANGE the equations and write them on TOP of each other so that the x and y variables line up:
`{{:(24 x + ay =-13),(6bx-5y=-9):}`
In a system of equations that has no solution, the x-coefficients must equal each other and the y-coefficients must equal each other. Thus, for the x - coefficients, `24=6b,` which means that `b =4.` for the y-coefficients, `a =-5.` The question asks for the value of `|a+b|, ` which is `|-5+4|=|-1|=1,` CHOICE (B). (Note that if you USED the EQUATION `-bx+5y=9,` you would get `a =5and b =-4,` which still result in the correct answer.)


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