C=2x+5y
Constraints:
x+y>=2
2x-3y<=-6
3x-2y>=6
A-42
B-4
C-49
D-10
I encountered this question while doing the Systems of Linear Equations and Inequalities test at http://www.classzone.com/books/algebra_2/chapterquiz_national.cfm. It seemed easy enough. So I graphed the inequalities on desmos.com and this is what I got: https://i.stack.imgur.com/tkLRS.png So I plugged (6,6) into C=2x+5y, and ended up with C=42. However, at the end of the test, it said that the correct answer is 4. I'm unsure what I did wrong, and hopefully you can explain it to me.
The answer should be $42$. We can see that $4$ is not correct as an answer because there is no $(x,y)\in\mathbb R$ such that $2x+5y=4$.
If $$2x+5y=4\iff y=-\frac{2}{5}x+\frac 45,$$then we have $$x+y\ge 2\iff x+\left(-\frac{2}{5}x+\frac 45\right)\ge 2\iff x\ge 2$$ and $$2x-3y\le -6\iff 2x-3\left(-\frac{2}{5}x+\frac 45\right)\le -6\iff x\le -\frac 98.$$ There is no $x\in\mathbb R$ such that "$x\ge 2\ \text{and}\ x\le -\frac 98$".
In the same way as above, we can see that there is no $(x,y)\in\mathbb R$ such that $2x+5y=10.$ On the other hand, since $2\times 6+5\times 6=42$, we can choose $42$ as an answer.