Question 340854
first problem:


x + y >= 14
y = x - 2


Substitute x-2 for y in the first equation to get:


x + x - 2 >= 14


Solve for x to get:


x >= 8


You do this by adding 2 to both sides of the equation and then combining terms on each side of the equation and then dividing both sides of the equation by 2.


Since y = x - 2, then y will always be 2 less than whatever x is.


Confirm by substituting for x and y in the original equation.


If x is greater than or equal to 8, the equation should be true, and if x is smaller than 8, the equation should be false.


Examples:


When x = 8, then y = 6, and x + y >= 14 becomes 14 >= 14 which is true.


When x = 6, then y = 4, and x + y >= 14 becomes 10 >= 14 which is false.


When x = 10, then y = 8, and x + y >= 14 becomes 18 >= 14 which is true.


second problem:


x + y <= 28
y = x + 8


Substitute x + 8 for y in the first equation to get:


x + x + 8 <= 28


Solve for x to get:


x <= 10


You do this by subtracting 8 from both sides of the equation and then combining like terms and then dividing both sides of the equation by 2.


Since y = x + 8, then y will always be 8 more than whatever x is.


Confirm by substituting for x and y in the original equation.


If x is smaller than or equal to 10, then the equation should be true.


If x is greater than 10, then he equation should be false.


Example:


When x = 10, y = 18, and x + y <= 28 becomes 28 <= 28 which is true.


When x = 12, y = 20, and x + y <= 28 becomes 32 <= 28 which is false.


When x = 8, y = 16, and x + y <= 28 becomes 24 <= 28 which is true.