Question

Which ordered pair makes both inequalities true? y < 3x – 1 y > –x + 4

Answer 1

(4,0) is the right option. hope it will help you!

Answer 2

we're proceeding to verify each case

we have

$y < 3x-1$ ------> inequality A

$y\geq -x+4$ -----> inequality B

Case A) point $(4,0)$

$x=4\\y=0$

Verify Inequality A

$y < 3x-1$

$0 < 3*4-1$

$0 < 11$ ------> is true

Verify Inequality B

$y\geq -x+4$

$0\geq -4+4$  

$0\geq 0$ -------> is true

therefore

the point $(4,0)$ is a solution

Case B) point $(1,2)$

$x=1\\y=2$

Verify Inequality A

$y < 3x-1$

$2 < 3*1-1$

$2 < 2$ ------> is not true

Verify Inequality B

$y\geq -x+4$

$2\geq -1+4$  

$2\geq 3$ -------> is not true

therefore

the point $(1,2)$ is not the solution

Case C) point $(0,4)$

$x=0\\y=4$

Verify Inequality A

$y < 3x-1$

$4 < 3*0-1$

$4 < -1$ ------> is not true

Verify Inequality B

$y\geq -x+4$

$4\geq -0+4$  

$4\geq 4$ -------> is true

therefore

the point $(0,4)$ is not the solution

Case D) point $(2,1)$

$x=2\\y=1$

Verify Inequality A

$y < 3x-1$

$1 < 3*2-1$

$1 < 5$ ------> is true

Verify Inequality B

$y\geq -x+4$

$1\geq -2+4$  

$1\geq2$ -------> is not true

therefore

the point $(2,1)$ is not the solution

therefore

the answer is

$(4,0)$