Pearson Algebra 1 Common Core, 2011
PA
Pearson Algebra 1 Common Core, 2011 View details
6. Systems of Linear Inequalities
Continue to next subchapter

Exercise 3 Page 402

There are two constraints in this problem. The first being the budget and the second being the amount of fruit needed.

Fruit Constraint

Let represent the and the We need to buy at least of fruit. We can express the total amount of fruit we buy as an inequality.

Budget Constraint

The cost and the set us back Let's write an expression for the total amount of money we spend on fruit.
We also know that our total spending cannot exceed which can be described as the following inequality.

System of Inequalities

Combining our inequalities, we get a system of inequalities.
To graph this we need to identify the boundary lines. To do that we have to solve each of them for
Solve for
Let's start with the first inequality. We have a slope of and a intercept of Let's draw the graph of a linear function with these characteristics.
Diagram showing the graph of g=-1.6c+6

The inequality sign tells us that is less than or equal to the line. Therefore, we know that our boundary is a solid line and that we should shade the area below the line. When graphing we must keep in mind that and cannot take negative values.

Diagram showing the solutions to inequality of g less than or equal to -1.6c+6

Let's continue with the second inequality. The boundary line has a slope of and a intercept of We know that is greater than or equal to the line. The boundary line must then be a solid line and we need to shade the area above the line.

Diagram showing the solutions to g less than or equal to -1.6c+6 and g greater than or equal to -c+4 overlapping each other

The common solutions for the given system lie where the shaded regions overlap. They are bounded by the boundary lines and the vertical axis.