Is (4, 1) a solution to this system of inequalities? x ≥ 4 x + 7y ≤ 11

Mathematics

2 answers:

Naya [18.7K]3 years ago

6 0

Yess!!!!!!!!!!!!!!!!!!!!

My name is Ann [436]3 years ago

4 0

<h3>Answer: Yes (4,1) is a solution</h3>

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Explanation:

Plug (x,y) = (4,1) into the first inequality

We replace x with 4. There is no y value to worry about here.

After doing so, x ≥ 4 turns into 4 ≥ 4 which is a true statement.

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Plug (x,y) = (4,1) into the second inequality

x + 7y ≤ 11 turns into 4 + 7(1) ≤ 11 which simplifies to 11 ≤ 11

This is also a true statement.

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Both inequalities result in true statements after plugging in (x,y) = (4,1). Therefore, (4,1) is a solution.

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Step-by-step explanation:

The answer is quadrant two because the answer is in the form of -x,y. When the x is negative and the y is positive, it is always going to be in quadrant 2. As you can see in the image below, quadrant 1 is going to be all positive, quadrant two is going to be negative then positive, quadrant three is going to be all negative, and quadrant 4 is going to be positive then negative. Use this as a guide for the rest of your question. I hope this helps!