Algebra Unit 6 Systems of Equations and Inequalities

What is the best method to solve this system of equations?

5x - 4y = 11

5x + 4y = -14

• Graphing

• Substitution

• Elimination

• Connection

Where did the error occur in this problem?

• There is no error, the solution is (59,13)

• The wrong equation was used to solve for x.

• When solving for y, 14 should have been subtracted instead of added.

• When solving for x, 13 should have been divided instead of multiplied.

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40

Using the substitution method, what goes in the parentheses to solve this system?

Which equation results from adding these if solving by elimination?

• -8y = 28

• -8y = -25

• 10x = -3

• 10x - 8y = -3

Is this a system of equations or a system of inequalities?

• System of Inequalities

• System of Equations

• Neither

• Both

Is this a system of equations or a system of inequalities?

• System of Inequalities

• System of Equations

• Neither

• Both

FroYo Express charges $5.75 for a large cup of frozen yogurt and $0.25 for each topping. The Big Chill charges $2.75 for a large cup of frozen yogurt and $1.25 for each topping. The graph represents the relationship between the number of toppings, x, and the total cost of a large cup of frozen yogurt, y, at the two stores. When will the cost be the same at both stores?

• The cost is the same at both stores when 6.5 toppings are ordered.

• The cost is the same at both stores when 3 toppings are ordered.

• The cost is the same at both stores when 5.75 toppings are ordered.

• The cost is the same at both stores when 2 toppings are ordered.

A system of inequalities is shown.

x + y < 2

x - y ≤ -1

Which region best represents the solution set for this system of inequalities?

• Region A

• Region B

• Region C

• Region D

Which of the following points lies in the solution set to the graphed system of linear inequalities?

• (-4, 6)

• (-8, -8)

• (6, 4)

• (7, -3)