Question

If 2|x|-|y|=3 and 4|x|+|y|=3, then find the possible order pairs of the form (x,y).​

Answer 1

I assume you want solutions, thats what the question means by ordered pairs,

You can do easily such problems by inspection ( dangerous if you dont have practice ) or graphing it would be the safest way.

I assume you are just a beginner and i want to provide an answer so that you no longer asks such questions again.

I am not going to do the solution, but i will give you hints. You note that if you master how to graph such things this would be a piece of cake for you..

Alright by f(x) = |x| we mean that our value is +x when x>0 and -x when x<0. So for example, if we put 1 in our function we get out put 1 but if it it is -1 we get -(-1) = 1, it appears for beginners that mod always only allows positive numbers to be out but there is also an deeper meaning w.r.t to functions. Coming to your question, it is pretty easy to graph y = 2x - 3 , alright now figure out all the conditions,  

• x>0 y>0 ---> y = 2x - 3
• x<0 y>0 ---> y = -2x - 3
• x>0 y<0 ---> -y = 2x -3
• x<0 y<0 ---> -y= -2x - 3

You could also think of quadrants, for the above equation, right??

So for the first quadrant sketch y= 2x - 3 ( only the part lying on first quadrant ) and similarly do the same for rest of all.

DO the same for the second 4x + y = 3 equation and find the intersection, It is just an exercise to get familiarised with  these graphing but in an exam situation its upto your smartness....smartness also means how fast you eliminate unwanted parts of the graph. Nice question! When one gets enough practice things flow quickly as water.