# x+2y is less than or equal to 4 and x-y is greater than 6Graphing solutions

Asked on by loriu

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to solve the system of inequalities `x+2y<=4`  and `x-ygt6` , hence you should isolate y in both inequalities to the left side such that:

`2y<= 4 - x =gt y<= 2 - x/2`

`x - y gt 6 =gt -y gt 6 - x =gt y lt x - 6`  (notice that multiplication by -1 changes the direction of inequality)

You should sketch both lines `y = 2 - x/2`  and `y = x - 6`  such that:

Notice that for inequality `y<= 2 - x/2` , the region found to the left of the red line comprises the values that check the inequality and  for the inequality `y lt x - 6` , the  region found to the right of black line comprises the values that check the inequality.

The solution to the system of inequalities is the common region to both inequalities, hence, this region is found below the point of intersection of lines, between the black and red lines.

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