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# Math question

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Hi guys! I am not sure how to solve this type of question:

$$\text{Given that }-3 \le 7x + 2y \le 3\text{ and }-4 \le y - x \le 4,\text{ what is the maximum possible value of }x + y?$$

May 17, 2019
edited by Guest  May 17, 2019

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Worked out how to do it myself - sorry for any inconvenience.

To solve this problem, we need to get x+y expressed in an inequality so we can work out the maximum possible value. In order to do that, we need $$x\&y$$ to have an equal coefficient.

Let's multiply the first inequality by 2: $$(-3\le7x+2y\le3)\times2=-6\le14x+4y\le3.$$

Now we need to multiply the second inequality by 5: $$(-24\le y-x\le4)\times5=-20\le5y-5x\le20.$$

Now we can add both inequalities. Note that we can only do this if the signs on the inequalities are the same, but, since they are, we are all good.

$$(-20\le5y-5x\le20)+(-6\le14x+4y\le3)=-26\le9x+9y\le26.$$

Now we can isolate x+y by dividing the expression by 9: $$(-26\le9x+9y\le26)\times9=-\dfrac{26}{9}\le x+y\le\dfrac{26}{9}.$$

Since the highest value of the inequality is $$\dfrac{26}{9}$$, the maximum possible value of x+y is $$\dfrac{26}{9}.$$

/ᐠ｡ꞈ｡ᐟ\/ᐠ｡ꞈ｡ᐟ\/ᐠ｡ꞈ｡ᐟ\

May 17, 2019