Question

Which points are solutions of the system? x>3 y< or equal to 2x-5 Choose all answers that are correct (4,-4) (4,8) (5,10) (6,0) (6,-2)

Answer 1

(4,-4), (6,0), (6,-2)

Explanation:

Just substitute each ordered pair to the given. If the output of both inequalities are true, then the point is a solution to the system.

True inequalities will be colored blue will false inequalities will be colored red.

(4,-4)

`x>3`
`color(blue)(4>3)`

`y<=2x-5`
`-4<=2(4)-5`
`-4<=8-5`
`color(blue)(-4<=3)`

(4,-4) is a solution.

(4,8)

`4>3`
`color(blue)(4>3)`

`y<=2x-5`
`8<=2(4)-5`
`8<=8-5`
`color(red)(8<=3)`

(4,8) is not a solution.

(5,10)

`5>3`
`color(blue)(5>3)`

`y<=2x-5`
`10<=2(5)-5`
`10<=10-5`
`color(red)(10<=5)`

(5,10) is not a solution.

(6,0)

`x>3`
`color(blue)(6>3)`

`y<=2x-5`
`0<=2(6)-5`
`0<=12-5`
`color(blue)(0<=7)`

(6,0) is a solution.

(6,-2)

`x>3`
`color(blue)(6>3)`

`y<=2x-5`
`-2<=2(6)-5`
`-2<=12-5`
`color(blue)(-2<=7)`

(6,-2) is a solution.