Equality Constraints Quiz

Solving linear equations with equality constraints: What is the solution to the equation 2x + 3y = 12 when y = 2?

• The solution is x = 3.

• The solution is x = 4.

• The solution is x = 2.

• The solution is x = 6.

Solving linear equations with equality constraints: Solve the equation 4x - 2y = 10 for x when y = 3.

• x = 8

• x = 5

• x = 4

• x = 2

Solving linear equations with equality constraints: If 3x + 4y = 24, find the value of y when x = 4.

• y = 2

• y = 10

• y = 3

• y = 6

Solving linear equations with equality constraints: Determine the value of x in the equation 2x - 5y = 15 when y = 3.

• 20

• 15

• 10

• 5

Solving linear equations with equality constraints: What is the solution to the equation 4x + 7y = 35 when y = 5?

• x = 5

• x = 3

• x = 7

• x = 0

Identifying feasible regions: Which of the following points is in the feasible region for the inequalities x + y ≤ 10 and 2x - y ≥ 4?

• Option A: (3, 7)

• Option B: (2, 3)

• Option A: (5, 6)

• Option C: (8, 2)

Identifying feasible regions: Identify the feasible region for the inequalities 3x + 2y ≤ 12 and x - y ≥ 5.

• Feasible region is the area above the line 3x + 2y = 12 and to the left of the line x - y = 5.

• Feasible region is the area to the left of the line 3x + 2y = 12 and below the line x - y = 5.

• Feasible region is the area below the line 3x + 2y = 12 and to the right of the line x - y = 5.

• Feasible region is the area to the right of the line 3x + 2y = 12 and above the line x - y = 5.

Identifying feasible regions: Determine the feasible region for the inequalities 2x + 3y ≤ 18 and x + y ≥ 6.

• Feasible region is the area where the shaded regions of both inequalities do not overlap.

• Feasible region is the area where the shaded region of only the second inequality is located.

• Feasible region is the area where the shaded region of only the first inequality is located.

• Feasible region is the area where the shaded regions of both inequalities overlap.

Identifying feasible regions: Which of the following points is not in the feasible region for the inequalities 4x - 3y ≤ 12 and 2x + y ≥ 8?

• Option A: (2, 5)

• Option C: (0, 0)

• Option B: (1, 7)

• Option A: (3, 4)

Identifying feasible regions: Identify the feasible region for the inequalities 5x - 2y ≤ 10 and 3x + 4y ≥ 12.

• Feasible region is the area where only one inequality is satisfied.

• Feasible region is the area where neither inequality is satisfied.

• Feasible region is the area where only the first inequality is satisfied.

• Feasible region is the shaded area where both inequalities are satisfied.