Greg and George bought shoes at a local store. Greg bought one dress shoe and 4 sneakers and spent less than $400.
George bought one dress shoe and 6 sneakers and spent more than $400.
Inequality signs < and > denote less than and greater than respectively.
To solve the above inequalities in order to find x and y prices, a pair of solutions will be the result since linear inequalities with two variables will have a range of solutions
In other words, to find x and y for the inequalities we find a point (x,y) that satisfies the inequality.
Example: if the price of a dress shoe is $80 and the price of a sneaker is $60, it satisfies the system of inequalities for Greg and George since their shoe expenses stay below and above $400 respectively.
We could then say that the point (80,60) is one of the solutions to the inequalities.
We could graph the inequalities in order to find points on the graph that satisfy the inequalities. To graph the inequality we make the equation a linear equation x+4y=400 and plot a straight line in accordance to the inequality. All points above the line satisfy George's inequality and vice versa.
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