Let x be the number of pounds of chicken and y be the number of pounds of steak. We are told that the price per pound of chicken is 1.29 and that the pricer per pound of steak is 3.49. Note that if we want to calculate the price of x pounds of chicken, we multiply this quantity by the price per pound and it will give us the cost. So we have that
represents the total cost for x poiunds of chicken and
represents the total cost for y pounds of steak.
Since we only have 100 available for the barbecue, this means that the total cost should be less than or equal to 100. So if we add these two quantities, it should be less than 100. This leads to the inequality
If we graph this using a graphing software, we get
where x and y should be non negative numbers. Any point that lays on the green area is a solution. For example if we take x=1 and y=1 we get that the total cost is 4.78, which is less than 100.