Question

Which of the following points would be a solution to this system of linear inequalities? ​

Answer 1

Let's plug in both x and y values in the equation and check if the inequality is true...

$\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}$

$(4,1) \\ y \leqslant x + 1 \\ y < - \frac{x}{2} - 1$

Substitute x as 4 and y as 1

$1 \leqslant 4 + 1 \\ 1 < - \frac{4}{2} - 1$

$0 \leqslant 4 + 1 \\ 1 < - 2 - 1$

$0 \leqslant 5 \\ 1 < - 3$

• This is not a solution because both are not true, Only one equation is giving true as answer which is not correct!~

$\purple{ \rule{300pt}{3pt}}$

$(0, - 3) \\ y \leqslant x + 1 \\ y < - \frac{x}{2} - 1$

Substitute x as 0 and y as -3

$- 3 \leqslant 0 + 1 \\ - 3 < - \frac{0}{2} - 1$

$- 3 \leqslant 1 \\ - 3 < - 0 - 1$

$- 3 \leqslant 1 \\ - 3 < - 1$

• This is a solution because both are true, Both the equations are true which means the ordered pair is a solution!~

Thus, Option B (0,-3) is the correct choice....