Question

Determine which point is a solution to the system
y s -4x + 3
by >
> 3x - 3

Answer 1

The point is (0, 0).

Explanation:

We'll test all the points in the given equations:

→ (0, -3):

`\begin{cases} y\le-4x+3 \\ -3\le-4\cdot0+3\\ -3\le0+3\\ -3\le3\Longrightarrow True!\end{cases} \begin{cases} y>3x-3\\ -3> 3\cdot0-3\\ -3>0-3\\ -3>-3\Longrightarrow False!\end{cases}`

→ (0, 0):

`\begin{cases} y\le-4x+3 \\ 0\le-4\cdot0+3\\ 0\le0+3\\ 0\le3\Longrightarrow True!\end{cases} \begin{cases} y>3x-3\\ 0>3\cdot0-3\\ 0>0-3\\ 0>-3\Longrightarrow True!\end{cases}`

→ (1, -2):

`\begin{cases} y\le-4x+3 \\ -2\le-4\cdot1+3\\ -2\le-4+3\\ -2\le-1\Longrightarrow True!\end{cases} \begin{cases} y>3x-3\\ -2>3\cdot1-3\\ -2>3-3\\ -2>0\Longrightarrow False!\end{cases}`

→ (1, 2):

`\begin{cases} y\le-4x+3 \\ 2\le-4\cdot1+3\\ 2\le-4+3\\ 2\le-1\Longrightarrow False!\end{cases} \begin{cases} y>3x-3\\ 2> 3\cdot1-3\\ 2>3-3\\ 2>0\Longrightarrow True!\end{cases}`

The single point that obeys both inequalities is (0, 0).