Question

The sum of two positive integers, x and y, is not more than 40. The difference of the two integers is at least 20. Chaneece chooses x as the larger number and uses the inequalities y<=40-x and y<=x-20

Answer 1

Answer: No, Chaneece mixed up the variables. The correct solution is that x must be between 20 and 40 and y must be between 0 and 20.

Explanation:

Answer 2

The value of x lies between 20 and 40 and value of y lies between -20 and 10

Explanation:

We are given that

`y\leq 40-x`....(1)

`y\leq x-20`...(2)

First we convert inequality equation into equality equation to find the solution of the given system of inequality equation.

Therefore, we can write as

`y=-x+40`...(3)

`y=x-20`...(4)

Adding equation (3) and (4) we get

`2y=20`

`y=10`

Substitute y=10 in equation (3) we get

`10=40-x`

`x=40-10=30`

(30,10) is the intersect point of two equation.

Put x=0 in equation (3)

`y=40`

Substitute y=0 in equation (3)

`x=40`

Substitute x=0 in equation (4)

`y=-20`

Substitute y=0 in equation (4)

`x=20`

Substitute x=0 and y=40 and in equation (1)

`40\leq 40`

Hence, the equation is true.Therefore, the shaded region below the line.

Substitute x=0 and y=-20 in equation (2)

`-20\leq -20`

The equation is true. Hence, the shaded region is below the line.

Hence, the value of x lies between 20 and 40 and value of y lies between -20 and 10.