Question 178535
Tickets to a concert cost $25 for lower-level seats and $10 for upper-level seats.
A company plans to buy up to 30 tickets for employees and spend up to $500. Write
and graph a system of linear inequalities to represent all the possible combinations of lower-level and upper-level tickets the company can buy. 
I got: x + y is less than or equal to 30
25x + 10y is less than or equal to 500 
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Solve each for y and then graph.
x>=0
y>=0
y <= 30 - x
y <= (-5/2)x + 50
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Graph the equalities as they are the boundary of the inequalities.
Graph y = -x+30 and y = (-5/2)x + 50
{{{graph(400,300,-10,100,-10,100,-x+30,(-5/2)x+50)}}}
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Shade the halfplane BELOW the line as you want "less than"
Shade the halfplan BELOW the 2nd line for the same reason.
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The solution set is the set of all points that satisfy both conditions.
Since x and y are not negative the points are restricted to Quadrant I.

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Cheers,
Stan H.