Question

draw a graph of the equation 3x-2yand x+y=3 (in same graph) and shade the region between the lines and y-axis​

Answer 1

CORRECT QUESTION.

Draw a graph of the equation 3x - 2y = 4  and  x + y = 3 (in same graph) and shade the region between the lines and y-axis.

EXPLANATION.

Graph of the equation,

(1) = 3x - 2y = 4.

As we know that,

Put the value of x = 0 in equation, we get.

⇒ 3(0) - 2y = 4.

⇒ 0 - 2y = 4.

⇒ -2y = 4.

⇒ y = -2.

Their Co-ordinates = (0,-2).

Put the value of y = 0 in equation, we get.

⇒ 3x - 2(0) = 4.

⇒ 3x = 4.

⇒ x = 4/3.

⇒ x = 1.33.

Their Co-ordinates = (1.33,0).

(2) = x + y = 3.

As we know that,

Put the value of x = o in equation, we get.

⇒ 0 + y = 3.

⇒ y = 3.

Their Co-ordinates = (0,3).

Put the value of y = 0 in equation, we get.

⇒ x + 0 = 3.

⇒ x = 3.

Their Co-ordinates = (3,0).

Both the curves intersects at a point = (2,1).

Answer 2

Gɪᴠᴇɴ :

➣ Two equations as,

1. 3x - 2y = 4 -----(1)
2. x + y = 3-----(2)

Cᴀsᴇ - 1 :

Lᴇᴛ,

➣ Assume the equation (1), to calculate points on both x-axis & y-axis.

$\red\checkmark\:\:\bf{3x\:-\:2y\:=\:4}$

❶ Substituting x = 2 in the above equation, we get

$\implies\:\:\rm{3\times{2}\:-\:2y\:=\:4}$

$\implies\:\:\rm{2y\:=\:6\:-\:4}$

$\implies\:\:\rm{2y\:=\:2}$

$\implies\:\:\bf{y\:=\:1}$

❷ Substituting x = 0 in that equation, we get

$\implies\:\:\rm{3\times{0}\:-\:2y\:=\:4}$

$\implies\:\:\rm{2y\:=\:-\:4}$

$\implies\:\:\bf{y\:=\:-2}$

Hᴇɴᴄᴇ,

➣ Points of the equation are as shown in the below table.

$\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 2 & \sf 1 \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf -2 \end{array}}$

➣ Now draw a graph using the points (2 , 1) & (0 , -2).

Cᴀsᴇ - 2 :

Lᴇᴛ,

➣ Assume the equation (2), to calculate points on both x-axis & y-axis.

$\red\checkmark\:\:\bf{x\:+\:y\:=\:3}$

❶ Substituting x = 0 in the above equation, we get

$\implies\:\:\rm{0\:+\:y\:=\:3}$

$\implies\:\:\bf{y\:=\:3}$

❷ Substituting y = 0 in that equation, we get

$\implies\:\:\rm{x\:+\:0\:=\:3}$

$\implies\:\:\bf{x\:=\:3}$

Hᴇɴᴄᴇ,

➣ Points of the equation are as shown in the below table.

$\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 3 \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 3 & \sf 0 \end{array}}$

➣ Now draw a graph using the points (0 , 3) & (3 , 0).