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

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)

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