Solving Equations and Inequalities

Which of the following is a solution to the systems of inequalities?

• (0, 3)

• (-3, 2)

• (1,4)

• (-1, 0)

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

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

• 4A + 6B = 3

  $13.50A - $13B = 6

• A + B = 4

  A - B = 6

• 4A + 6B = $13

  3A + 7B = $13.50

• 4A - 6B = $13

  3A - 7B = $13.50

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.

Which of the following is a solution to the systems of inequalities?

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)

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