How do you solve directly for the variable X in a system of linear inequalities?

Question

X<A,

BX+CY>D,

Y>F

 

Answer 1

The solution to a systems of inequalities is a region NOT a point like the solution to a system of equations.

The three inequalities you have (X<A, BX+CY>D, Y>F) are all regions divided by a line.

X<A is the regions bounded by the vertical line X=A which passes through the point (A,0).  The solution is the area to the left the line since X is less than A

Y>F is the regions bounded by the horizontal line Y=F which passes through the point (0,F).  The solution to this is the area above the line since Y is greater than F

BX+CY<D is a region bounded by the slanted line BX+CY=D which, if you want, you can put into slope-intercept form (y=mx+b) in this case we would need to solve for Y.  Doing so gives Y>(-B/C)X+D/C. So the slope is (-B/C) and the Y-intercept is (D/C).

If you had actual numbers instead of letters you would be able to graph all of this and you could shade the region that satisfies all of the inequalities.