Question

Which ordered pair is a solution to the system

{y,x-1
{y>-x+2

(4,0)
(0,0)
(1,-3)
(-2,3)

Answer 1

`(4,0)`

Explanation:

we have

`y<x-1` -----> inequality A

`y>-x+2` -----> inequality B

we know that

If a ordered pair is a solution of the system of equations , then the ordered pair must satisfy both inequalities

Verify each case

case A)
`(4,0)`

Inequality A

`0<4-1`

`0<3` ------> is true

Inequality B

`0>-4+2`

`0>-2` -------> is true

therefore

the ordered pair is a solution

case B)
`(0,0)`

Inequality A

`0<0-1`

`0<-1` ------> is not true

therefore

the ordered pair is not a solution

case C)
`(1,-3)`

Inequality A

`-3<1-1`

`-3<0` ------> is true

Inequality B

`-3>-1+2`

`-3>1` -------> is not true

therefore

the ordered pair is not a solution

case D)
`(-2,3)`

Inequality A

`3<-2-1`

`3<-3` ------> is not true

therefore

the ordered pair is not a solution