SOLUTION: I need help with this open ended system of linear inequality! You are buying movie passes and gift certificates as prizes for an event. You need at least 5 movie passes and 2 gif

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Question 710791: I need help with this open ended system of linear inequality!
You are buying movie passes and gift certificates as prizes for an event. You need at least 5 movie passes and 2 gift certificated. A movie pass costs $6.00 and a gift certificate costs $10.00. The most you can spend is $70.00. write a system of linear inequalities that shows the number of movie passes (x) and gift certificates (y) that can be purchased. Graph the system. Use the graph to determine if you can buy 6 movie passes and 3 gift certificates. Please explain your answer.
Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website!
EDITED: Added derivation of slope-intercept form.
EDIT: Beware Unknown Possible Mistake in Solution.

Build a cost equation. Maybe try like, x movie passes, y gift certificates.
How many of them you buy must not be more than $70.

You also have some conditions:
and

Graph those three inequalities and you can read your desired choices directly on the graph. Putting the cost equation into simplified, slope intercept form may be useful.
Changinge the standard form to slope-intercept form:
10y<=-6x+70
5y<=-3x+35

Try the graph. There seem to be [seven] points for x and y that satisfy the problem description. You're only interested in the integer coordinates (x,y) in the region.