Question

Which ordered pair makes both inequalities true? y < 3x – 1 y > –x + 4 On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (0, negative 1) and (1, 2). Everything to the right of the line is shaded. The second solid line has a negative slope and goes through (0, 4) and (4, 0). Everything above the line is shaded.

Answer 1

None of the options is true

Explanation:

Given

`y &lt; 3x - 1`

`y &gt; -x + 4`

Required

Which makes the above inequality true

The missing options are:

`(4,0)\ (1,2)\ (0,4)\ (2,1)`

`(a)\ (x,y) = (4,0)`

Substitute values for x and y in the inequalities

`y &lt; 3x - 1`

`0<3*4 - 1`

`0<12 - 1`

`0<11` ---- This is true

`y &gt; -x + 4`

`0 > -4 + 4`

`0 > 0` --- This is false

`(b)\ (x,y) = (1,2)`

Substitute values for x and y in the inequalities

`y &lt; 3x - 1`

`2<3 * 1 - 1`

`2<3 - 1`

`2<2` --- This is false (no need to check the second inequality)

`(c)\ (x,y) = (0,4)`

Substitute values for x and y in the inequalities

`y &lt; 3x - 1`

`4< 3*0-1`

`4< 0-1`

`4<-1` --- This is false (no need to check the second inequality)

`(d)\ (x,y) = (2,1)`

Substitute values for x and y in the inequalities

`y &lt; 3x - 1`

`1<3*2-1`

`1<6-1`

`1<5` --- This is true

`y &gt; -x + 4`

`1 > -2+4`

`1 > 2` -- This is false

Hence, none of the options is true