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



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