Can this system of inequalities be solved for x?

[annamal]

Summary: Can these two equations be solved for x like a system of linear inequalities, and how?
$x- 2y \le 54$
$x + y \ge 93$

We start with
$x- 2y \le 54$
$x + y \ge 93$

Multiplying the second equation by 2, we have $2x + 2y \ge 184$. We cannot seem to cancel the y out with the first equation because that would create an unclear inequality. So how do we solve it algebraically?

MENTOR NOTE: Moved to Precalculus Homework Help hence no template.

 

[malawi_glenn]

Draw the individual inequalities as straight lines in the xy-plane.
How can you use this to figure out when both your inequalities are satisfied?
Is there a single x-value, or does it depend on y?

 

[annamal]

Draw the individual inequalities as straight lines in the xy-plane.
How can you use this to figure out when both your inequalities are satisfied?
Is there a single x-value, or does it depend on y?

That is solving it graphically. I would like to solve it algebraically.

 

[jedishrfu]

Start with the equalities first to find a common x,y that solves them.

BEFORE WE GO ANY FURTHER: PLEASE SHOW SOME WORK.

 

[malawi_glenn]

The graphical solution will just be an aid for your algebra

 

[FactChecker]

Summary: Can these two equations be solved for x like a system of linear inequalities, and how?
$x- 2y \le 54$
$x + y \ge 93$

You don't want to "solve" for x and y. Because these inequalities define two entire regions (half planes), not two thin lines with one intersection point.
y=13 and x=80 is the solution of x-2y=54; x+y=23. That doesn't tell you much.
Instead, you want to graph the lines x-2y=54; x+y=23 to see what the two regions (half planes) of the two inequalities are. Then you can see where the regions overlap. All the (x,y) points in the overlap are the answer.