solve the system y=ax+b, y=absolute value cx+d

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solve the system y=ax+b, y=absolute value cx+d

Mathematics
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You should identify the fact that \[y=|cx+d|=\sqrt{(cx+d)^2}\] by definition.
Just wait - I want to see if there's an easier way...but this way will work.
I'll just keep going. From the definition above, expand the radicand and square both sides to get rid of the square root. Then\[y^2=c^2x^2+2cdx+d^2\]

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Now, square both sides of the other equation,\[y^2=a^2x^2+2abx+b^2\]
scrap that - I always default to that method...easier to do the following...
Case-by-case method: \[y=|cx+d|=cx+d _.or_.-(cx+d)\]
Then, you go about it like you would with other linear equations. You want to find all x such that the same y is yielded. This occurs when,\[ax+b=cx+d_.or_.ax+b=-cx-d\]
Solving the first:\[x(a-c)=d-b \rightarrow x=\frac{d-b}{a-c}\]
and solving the second,\[x(a+c)=-d-b \rightarrow x= -\frac{b+d}{a+c}\]
cool thank you.
You're welcome...feel free to 'fan' me ;)

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