The best way to solve this problem is by plugging in each answer choice for both equations and seeing which one works. You can already see that choice A doesn't work because -1 is not greater than or equal to 4. That means you just need to test choices B and C!
Choice B (4, -2)
![x + y \geq 6\\ 4 + -2 \geq 6\\ 2 \geq 6](https://img.qammunity.org/2019/formulas/mathematics/high-school/yz020xlb5v25f432rnx5sg6d3e2wjxqrjc.png)
2 is not greater than or equal to 6, so choice B doesn't work.
Choice C (4, 2)
![x + y \geq 6\\ 4 + 2 \geq 6\\ 6 \geq 6 \\\\ x \geq 4\\ 4 \geq 4](https://img.qammunity.org/2019/formulas/mathematics/high-school/qt8rih2zxwczfn5g7oz7rkia61apodadrg.png)
Since 6 is equal to 6 and 4 is equal to 4, choice C works!
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Answer: C) (4, 2)