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# Absolute value

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Solve for x and y:

|x|+x+y=14

x+|y|-y=18

Sep 25, 2021

#1
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We will need to use these ideas:  If  x >= 0  then  |x| = x.

If  x < 0    then  |x| = -x.

If  y >= 0  then  |y| = y.

If  y < 0    then  |y| = -y.

If  x >= 0  and  y >= 0,  then:  |x| + x + y  =  14   --->   x + x + y  =  14   --->   2x + y  =  14

x + |y| - y  =  18   --->     x + y - y  =  18   --->           x  =  18

Solving this system, we find that  x = 18  and  y = -22  (but this answer is impossible because y was assumed to be >= 0.

If  x >= 0  and  y < 0, then  |x| + x + y  =  14   --->   x + x + y  =  14   --->   2x + y  =  14

x + |y| - y  =  18   --->      x - y - y  =  18   --->    x - 2y  =  18

Solving this system, we find that  x = 9.2  and  y = -4.4.

Now, do a similar analysis for the other two possibities (when x < 0) to get your final answer.

Sep 26, 2021
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