Question

Which of the following is the solution to the following system of inequalities?Let the green region represent the answer region.x+2y <=43x - y< =2

Answer 1

B

1) The way we're going to tackle this question is at first treating each inequality as an equation. So let's pick the first inequality, rewrite it as an equation set a t-table, and then trace a line.

2)

I) x+2y≤4

Rewriting it as a slope-intercept equation we get:

`x+2y=4\Leftrightarrow2y=4-x,\mathbf{y=2-(x)/(2)}`

Setting a t-table:

So we'll plot the following points: (-2,3), (-1, 2.5), (0, 2), (1, 1.5), (2, 1)

Similarly, we can do the same with the 2nd inequality:

3x-y≤2

`\begin{gathered} 3x-y=2 \\ -y=2-3x \\ y=3x+2 \end{gathered}`

Now, the t-table:

So the points we're going to use are: (-2,-4), (-1,-1), (0,2), (1,5), (2,8)

3) Now, let's treat them back as inequalities and plot them the solution will be on the darkest region, where the two regions overlap:

Examining the options, we can state the answer is: B