Question

3x+2y<0

answer and show work​

Answer 1

$\large\underline{\sf{Solution-}}$

Given linear inequality is

$\rm \: 3x + 2y < 0$

Let first represent the above inequality in the form of equation. So, above inequality, in the form of equation is

$\rm \: 3x + 2y = 0$

Substituting 'x = 2' in the given equation, we get

$\rm \: 3 \times 2 + 2y = 0$

$\rm \: 6 + 2y = 0$

$\rm \: 2y = - 6$

$\bf\implies \:y = - 3$

Substituting 'y = 0' in the given equation, we get

$\rm \: 3x + 2 \times 0 = 0$

$\rm \: 3x + 0 = 0$

$\rm \: 3x = 0$

$\bf\implies \:x \: = \: 0$

Substituting 'x = 4' in the given equation, we get

$\rm \: 3 \times 4 + 2y = 0$

$\rm \: 12 + 2y = 0$

$\rm \: 2y = - 12$

$\bf\implies \:y = - 6$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 0 \\ \\ \sf 2 & \sf - 3\\ \\ \sf 4 & \sf - 6 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 0), (2 , - 3) & (4 , - 6).

Now, the given linear inequality divides the xy - plane in to two regions.

Now, to check out the solution, we check the point (1, 0) in the given inequality.

So, given inequality can be rewritten as

$\rm \: 3 \times 1 + 2 \times 0 < 0$

$\rm \: 3 + 0 < 0$

$\rm \: 3 < 0$

$\bf\implies \:(1,0) \: doesnot \: satisfy \: 3x + 2y < 0$

➢ See the attachment graph.