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:

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

Step-by-step 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.

Answer 2

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.

Step-by-step explanation: