Write a system of inequalities to represent the shaded portion of the graph.

The solution of the system of inequalities 3x > y and x + y ≤ 4 is graphed by the shaded region given.

Step-by-step explanation:

See the graph attached.

The dotted straight line passes through the points (0,0) and (3,1).

Therefore, the equation is {Using the two point form of equation of straight line}

⇒ 3y = x ........ (1)

Therefore, the shaded part of the graph holds the equation 3y > x {AS the shaded portion does not include the straight line (1)}

Again, the equation of the firm line is given by {Applying the intercept form of equation of straight line}

⇒ x + y = 4 ......... (2)

Therefore, the shaded region of the graph is represented by the equation  x + y ≤ 4 {Since, the shaded region includes the line also}

Therefore, the solution of the system of inequalities 3x > y and x + y ≤ 4 is graphed by the shaded region given. (Answer)

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

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