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)
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)
