Question

which system of linear inequalities has the point (2 ,1) in its solution set?

Answer 1

Answer:

The system of Linear equation is x + 2y ≤ 4 and 2x - y > 0

Step-by-step explanation:

Given: Point ( 2 , 1 )

To find: System of Linear Inequalities which contain given point in

              its solution set

There are 2 lines passing through point ( 2 , 1 )

So first we find the equation of both lines

Equation of line using Two-Point form is given by,

$(y-y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Equation of line 1 passing through ( 0 , 2 ) & ( 4 , 0 )

$(y-2)=\frac{0-2}{4-0}(x-0)$

$(y-2)=\frac{-2}{4}x$

$(y-2)=\frac{-x}{2}$

$y=\frac{-x}{2}+2$

$y+\frac{x}{2}=2$

$x+2y=4$ ....... (1)

Equation line 2 passing through ( 0 , 0 )  & ( 2 , 1 )

$(y-0)=\frac{0-2}{0-1}(x-0)$

$y=\frac{-2}{-1}x$

$y=2x$

$2x-y=0$ ....... (2)

Now from given graph is clear line 1 contain the given point and area shaded by it is toward origin then we have less than equal sign,

⇒ x + 2y ≤ 4

Line 2 is dotted line. So, it does not contain the given point and area shaded by it is toward 4th quadrant then we have greater than sign in it.

⇒ 2x - y > 0

Therefore, The system of Linear equation is x + 2y ≤ 4 and 2x - y > 0

Answer 2

Answer:

its the last one number 4

Step-by-step explanation: