Final answer:
After substituting the point (10, -2) into both inequalities of the system and finding that both results are true, we conclude that (10, -2) is a solution to the system.
Step-by-step explanation:
The student has asked if the point (10, -2) is a solution to the system of inequalities. First, let's substitute the x and y values into each inequality to check if they satisfy both.
For the first inequality: X - 6y > 5, substituting x=10 and y=-2 gives us 10 - 6*(-2) > 5 which simplifies to 10 + 12 > 5. This simplifies further to 22 > 5, which is true.
For the second inequality 7x + 2y > 4, substituting x=10 and y=-2 gives us 7*10 + 2*(-2) > 4 which simplifies to 70 - 4 > 4. This simplifies further to 66 > 4, which is also true.
Since (10, -2) satisfies both inequalities, it is indeed a solution to the system.