Determining Solutions for Systems of Inequalities

Mr. Allen explains how to determine if a point is a solution to a system of inequalities without graphing. He uses the substitution method to check if given points satisfy the inequalities. Through multiple examples, he demonstrates how to substitute values and verify if the resulting statements are true, emphasizing the need for both inequalities to be satisfied for a point to be a solution.

What method is used to determine if a point is a solution to a system of inequalities?

• Graphing

• Substitution

• Elimination

• Factoring

In the first example, what is the result of substituting x = 2 and y = -10 into the first inequality?

• -10 ≤ 3

• -10 < 3

• -10 = 3

• -10 > 3

Why is the point (2, -10) not a solution to the system of inequalities?

• It satisfies both inequalities.

• It does not satisfy the first inequality.

• It does not satisfy the second inequality.

• It satisfies neither inequality.

In the second example, what is the result of substituting x = 3 and y = 5 into the first inequality?

• 5 = 8

• 5 ≥ 8

• 5 < 8

• 5 ≤ 8

Does the point (3, 5) satisfy the second inequality in the second example?

• Not enough information

• No

• Yes

• Only partially

In the third example, what is the result of substituting x = 4 and y = 0 into the first inequality?

• 12 ≥ 12

• 12 > 12

• 12 < 12

• 12 ≤ 12

Does the point (4, 0) satisfy the second inequality in the third example?

• Not enough information

• Only partially

• No

• Yes

In the fourth example, what is the result of substituting x = 5 and y = -3 into the first inequality?

• -3 < 4

• -3 > 4

• -3 = 4

• -3 ≤ 4

Does the point (5, -3) satisfy the second inequality in the fourth example?

• Yes

• No

• Only partially

• Not enough information

What must be true for a point to be a solution to a system of inequalities?

• It must satisfy at least one inequality.

• It must satisfy the second inequality only.

• It must satisfy all inequalities.

• It must satisfy the first inequality only.