Question

Which of the tollowing systems of inequalities would produce the region indicated on the graph below? VW 11 O A. VS-x+4;y x+2; y> 0; x > 0 O c. VS-x+4;y Sx+2; y 2 0;x20 DVS +4v2x+2; y0;. > 0

Answer 1

From the given figure

The colored region is bounded by 4 lines

2 lines are the x-axis and y-axis

Since the shaded is over the x-axis and right the y-axis

Then the first two inequalities are

$\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}$

For the other two lines, since the shaded region is under both of them and the lines are not dashed lines

Then the signs of inequalities are

$\leq,\leq$

Since the first line passes through points (0, 2) and (1, 3), then its slope is

$\begin{gathered} m_1=\frac{3-2}{1-0} \\ m_1=1 \end{gathered}$

The equation of the first line is

$y=x+2$

Since the second line passes through points (0, 4) and (1, 3), then its slope is

$\begin{gathered} m_2=\frac{3-4}{1-0} \\ m_2=-1 \end{gathered}$

The equation of the second line is

$y=-x+4$

Then the inequalities of the two lines are

$\begin{gathered} y\leq x+2 \\ y\leq-x+4 \end{gathered}$

Then the correct answer is C