Solve absolute value inequality with x and yI have difficulties to solve this system of inequalities. Normally you would solve it like a normal system of equations just writing ≤ or ≥ instead of =. But these contain an absolute value which confuses me. The system I want to solve is this: { | x − y | ≤ 1 | x + y | ≤ 1 I would have written it like that { − 1 ≤ x − y ≤ 1 − 1 ≤ x + y ≤ 1 And by adding the inequalities I would obtain − 1 ≤ x ≤ 1. I can’t get y though.I don’t understand how my textbook got a third inequality out of the two initial ones { − 1 ≤ x − y ≤ 1 − 1 ≤ y − x ≤ 1 − 1 ≤ x + y ≤ 1 But with that they can solve the system like so: ( 1 ) + ( 3 ) : − 1 ≤ x ≤ 1 and ( 2 ) + ( 3 ) : − 1 ≤ y ≤ 1.

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Solve absolute value inequality with x and yI have difficulties to solve this system of inequalities. Normally you would solve it like a normal system of equations just writing   ≤ or   ≥ instead of   =. But these contain an absolute value which confuses me. The system I want to solve is this:      {                                    |          x          −          y                  |          ≤          1                                              |          x          +          y                  |          ≤          1                        I would have written it like that      {                            −          1          ≤          x          −          y          ≤          1                                      −          1          ≤          x          +          y          ≤          1                        And by adding the inequalities I would obtain   −  1  ≤  x  ≤  1. I can’t get y though.I don’t understand how my textbook got a third inequality out of the two initial ones      {                            −          1          ≤          x          −          y          ≤          1                                      −          1          ≤          y          −          x          ≤          1                                      −          1          ≤          x          +          y          ≤          1                        But with that they can solve the system like so:   (  1  )  +  (  3  )  :  −  1  ≤  x  ≤  1 and   (  2  )  +  (  3  )  :  −  1  ≤  y  ≤  1.

floygdarvn · Accepted Answer

Let   S be the set of points in the cartesian plane which solve the system. In the last line of your question you found that   S is contained (and not equal) to the square   [  −  1  ,  1  ]  ×  [  −  1  ,  1  ].Note that   |  x  −  y  |  ≤  1 is the strip between the lines   y  =  x  −  1 and   y  =  x  +  1.   |  x  +  y  |  ≤  1 is the strip between the lines   y  =  −  x  −  1 and   y  =  −  x  +  1. What is the intersection of these two strips? Make a drawing and you will find   S.

meindwrhc · Accepted Answer

The third equation comes from multiplying by a negative. The inequality   −  1  ≤  x  −  y  ≤  1 is equivalent to multiplying it through by a constant, like   −  1, yielding the inequality   1  ≥  y  −  x  ≥  −  1 (you must flip the signs when multiplying by a negative). If we want to keep the original phrasing and use a less than or equal to sign, we just shift the order, and the inequality becomes   −  1  ≤  y  −  x  ≤  1It&#039;s really similar to solving a system of equations where you would multiply the equation by a constant so that adding the equations cancels out a term. We did the exact same thing here, and the constant was   −  1.

Solve absolute value inequality with x and y I have difficulties to solve this system of inequaliti

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