Question

HELP ASAP PLEASE! 100 POINTS!

Answer 1

We will use graphical method to solve it.

The inequalities are

• y<2/3x
• y≥-x+2

Graph both

We can see that the solution region is rightwards

The solution is (1.2,0.8)

Option D as the intersection point is ahead 1 unlike option A

Answer 2

Given system of inequalities:

`\large\begin{cases}y < (2)/(3)x\\y\geq-x+2\end{cases}`

When graphing inequalities:

• < or > = dashed line
• ≤ or ≥ = solid line
• < or ≤ = shade below the line
• > or ≥ = shade above the line

`y < (2)/(3)x`

The slope of the first inequality is 2/3, therefore at x = 1, y = 2/3.

So the correct line for the first inequality is the dotted line with the shallower slope.

As the relation is < for this inequality, the shading should be below the dotted line.

`y\geq-x+2`

From inspection of the given graphs, the line of the second inequality (solid line) is the same in all graphs.

As the relation is ≥ for this inequality, the shading should be above the solid line.

Therefore, the only graph that satisfies these conclusions is graph D (attached).