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

Answer:

None of the options is true

Step-by-step explanation:

Given

$y < 3x - 1$

$y > -x + 4$

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

$y < 3x - 1$

$0$

$0$

$0$ ---- This is true

$y > -x + 4$

$0 > -4 + 4$

$0 > 0$ --- This is false

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

Substitute values for x and y in the inequalities

$y < 3x - 1$

$2$

$2$

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

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

Substitute values for x and y in the inequalities

$y < 3x - 1$

$4< 3*0-1$

$4< 0-1$

$4$ --- This is false (no need to check the second inequality)

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

Substitute values for x and y in the inequalities

$y < 3x - 1$

$1$

$1$

$1$ --- This is true

$y > -x + 4$

$1 > -2+4$

$1 > 2$ -- This is false

Hence, none of the options is true