The first inequality, 2x + y ≤ 8, can be rewritten in slope-intercept form as y ≤ -2x + 8. This inequality is a linear equation with a slope of -2 and a y-intercept of 8. The line is solid (not dashed) because the inequality includes the equal sign. Shade the area below the line to represent all the possible combinations of cupcakes and fudge that Michael can afford with $8.
The second inequality, x + y ≥ 4, can be rewritten in slope-intercept form as y ≥ -x + 4. This inequality is a linear equation with a slope of -1 and a y-intercept of 4. The line is solid (not dashed) because the inequality includes the equal sign. Shade the area above the line to represent all the possible combinations of cupcakes and fudge that feed at least four siblings.
The intersection of the two shaded regions is the solution set of the system of inequalities. This represents all the possible combinations of cupcakes and fudge that Michael can buy to feed at least four siblings, without spending more than $8.
Michael has $8 and wants to buy a combination of cupcakes and fudge to feed at least four siblings. Each cupcake costs $2, and each piece of fudge costs $1.
This system of inequalities models the scenario:
2x + y ≤ 8
x + y ≥ 4
Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set
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