Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Find one point that lies in the solution set of the following system of inequalities:

Y<(or equal)1/2x+6
y>-3x-1

justify answer

Sagot :

heyDB
Simplify the first inequality.

Multiply 1/2 by x to get (1/2)x. 
y≤(1/2)x+6 and y>−3x−1 

Simplify. 
y≤x/2+6 and y>−3x−1

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation. 
x/2+6≥y and y>−3x−1 

Because 6 does not contain the variable to solve for, move it to the right-hand side of the inequality by subtracting 6from both sides. 
x/2≥−6+y and y>−3x−1 

Multiply both sides of the equation by 2. 
x≥−6⋅(2)+y⋅(2) and y>−3x−1 

Multiply −6 by 2 to get −12. 
x≥−12+y⋅(2) and y>−3x−1 

Multiply y by 2 to get y(2). 
x≥−12+y(2) and y>−3x−1 

Multiply y by 2 to get y⋅2. 
x≥−12+y⋅2 and y>−3x−1 

Move 2 to the left of the expression y⋅2. 
x≥−12+2⋅y and y>−3x−1 

Multiply 2 by y to get 2y. 
x≥−12+2y and y>−3x−1 

Reorder −12 and 2y. 
x≥2y−12 and y>−3x−1 



Simplify the second inequality.

Because x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation. 
x≥2y−12 and −3x−1<y 

Since −1 does not contain the variable to solve for, move it to the right-hand side of the inequality by adding 1 to both sides. 
x≥2y−12 and −3x<1+y 

Divide each term in the inequality by −3. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign. 
x≥2y−12 and −3x/−3>1/−3+y/−3 

Cancel 3 in the numerator and denominator. 
x≥2y−12 and −(−1⋅x)>1/−3+y/−3 

Multiply −1 by x to get −1x. 
x≥2y−12 and −(−1x)>1/−3+y/−3 

Rewrite −1x as −x. 
x≥2y−12 and −(−x)>1/−3+y/−3 

Simplify
x≥2y−12 and x>−1/3+y/−3 


x≥2y−12 and x>−1/3−y/3 


Point of intersection: (-2, 5)
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.