Question

Graph the solution for the following system of inequalities. Click on the graph until the correct solution is displayed. y ≤ x x + y ≥ 1

Answer 1

(1,0) and (0.5,0.5)

Explanation:

Given :
`y \leq  x`

`x + y\geq 1`

To Find: Graph the solution for the following system of inequalities.

Solution:

Plot the given inequalities using graphing calculator.

Green shows
`y \leq  x`

Purple shows
`x + y\geq 1`

Refer the attached graph ,

Solutions : (1,0) and (0.5,0.5)

Verification:

`y \leq x`

Substitute(1,0)

`0 \leq 1` TRUE

Substitute (0.5,0.5)

`0.5 \leq 0.5` TRUE

`x + y\geq 1`

Substitute(1,0)

`1 + 0\geq 1`

`1 \geq 1` TRUE

`x + y\geq 1`

Substitute (0.5,0.5)

`0.5 +0.5\geq 1`

`1\geq 1` TRUE.

Hence verified.

Thus solution is (1,0) and (0.5,0.5)

Answer 2

we have that

y ≤ x
x + y ≥ 1

using a graph tool
see the attached figure

the solution is the shaded area