Unit 7, Lesson 8
Solving Problems with Systems of Linear Inequalities in Two Variables
Integrated Math 1
Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
A triathlon athlete swims at an average rate 2.4 miles per hour, and bikes at an average rate of 16.1 miles per hour. At the end of one training session, she has swum and biked more than 20 miles in total.
The inequality
Mai said, "I'm not sure the graph is right. For example, the point
Elena is considering buying bracelets and necklaces as gifts for her friends. Bracelets cost $3, and necklaces cost $5. She can spend no more than $30 on the gifts. Elena needs at least 7 gift items.
This graph represents the inequality
Let
A gardener is buying some topsoil and compost to fill his garden. His budget is $70. Topsoil costs $1.89 per cubic foot, and compost costs $4.59 per cubic foot.
Select all statements or representations that correctly describe the gardener's constraints in this situation. Let
The combination of 7.5 cubic feet of topsoil and 12 cubic feet of compost is within the gardener's budget.
If the line represents the equation
Graph of an inequality, origin O. Horizontal axis, topsoil, dollars per cubic foot, scale is 0 to 50, by 5’s. Vertical axis, compost, dollars per cubic foot, scale is 0 to 25, by 5’s. Dashed line starts at approximately 0 comma 15 and passes through 25 comma 5. The region below the dashed line is shaded.
Two inequalities are graphed on the same coordinate plane.
Which region represents the solution to the system of the two inequalities?
Two inequalities graphed on a coordinate plane, origin O. Both axes from negative 10 to 8, by 2’s. The first dashed line starts above the x axis and to the left of the y axis and goes through 0 comma 2 and 7 comma 0. The region below the dashed line is shaded blue. The second shaded line starts above the x axis and to the left of the y axis and goes through negative 6 comma 7, 1 comma 0, and 8 comma negative 7. The region below the dashed line is shaded. Region A labeled in Quadrant 1, Region B labeled in quadrant 2 between 2 dashed lines, striped. Region C labeled in Quadrant 3, blue and striped. Region D labeled in Quadrant 4, between 2 dashed lines, blue.
The combination of 5 cubic feet of topsoil and 20 cubic feet of compost is within the gardener's budget.
If the line represents the equation
Graph of an inequality, origin O. Horizontal axis, topsoil, dollars per cubic foot, scale is 0 to 50, by 5’s. Vertical axis, compost, dollars per cubic foot, scale is 0 to 25, by 5’s. Solid line starts at approximately 0 comma 15 and passes through 25 comma 5. The region below the line is shaded.