Question

Is (10,−2) a solution of the system x−6y>5 and 7x−2y≤4?

(a) Yes
(b) No

Answer 1

To determine if (10,-2) is a solution of the system x-6y>5 and 7x-2y<=4, we need to substitute the values of x and y into the equations and check if the inequalities hold true. Since one of the inequalities is false, (10,-2) is not a solution to the system.

Step-by-step explanation:

To determine if (10,-2) is a solution of the system x-6y>5 and 7x-2y<=4, we need to substitute the values of x and y into the equations and check if the inequalities hold true.

For x-6y>5, when we substitute x=10 and y=-2, we get 10-6(-2)>5 which simplifies to 10+12>5, giving us 22>5 which is true.

For 7x-2y<=4, when we substitute x=10 and y=-2, we get 7(10)-2(-2)<=4 which simplifies to 70+4<=4, giving us 74<=4 which is false.

Since one of the inequalities is false, (10,-2) is not a solution to the system. Therefore, the correct answer is (b) No.