Solve Lesson 2 Page 24 SBT Math 10 – Kite>

Topic

The solution domain of the inequality $$2x – 3y > 5$$ is a semi-plane (excluding the line $$d:2x – 3y = 5$$) that does not contain any of the following coordinates?

A. $$\left( {0;0} \right)$$ B. $$\left( {3;0} \right)$$ C. $$\left( {1; – 2} \right)$$ D. $$\left( { – 3; – 4} \right)$$

Detailed explanation

A. Substituting x = 0, y = 0 into the inequality 2x – 3y > 5, we get:

2.0 – 3.0 > 5 ⇔ 0 > 5 (absurd)

Hence the point with coordinates (0; 0) is not in the domain of the solution of the given inequality.

B. Substituting x = 3, y = 0 into the inequality 2x – 3y > 5, we get:

2.3 – 3.0 > 5 6 > 5 (satisfactory)

Therefore the point with coordinates (0; 0) belongs to the domain of the solution of the given inequality.

C. Substituting x = 1, y = – 2 into the inequality 2x – 3y > 5, we get:

2.1 – 3.(– 2) > 5 8 > 5 (satisfied)

Therefore, the point with coordinates (1; – 2) belongs to the domain of the solution of the given inequality.

D. Substituting x = – 3, y = –4 into the inequality 2x – 3y > 5, we get:

2.(– 3) – 3.(– 4) > 5 ⇔ 6 > 5 (satisfied)

Therefore, the point with coordinates (– 3; – 4) belongs to the domain of the solution of the given inequality.

Choose A