Question

Which ordered pairs represent solutions to the linearinequality below? Check ALL that apply.x – 4y <-12 (Select all that apply.)(1,-8)(-8,-3)(-12,0)(3,5)(-7,9)(-4,2)

Answer 1

Given inequality:

x - 4y < -12

To check which is the solution of he given inequality : Substitute the given value of x & y if, they satisfy the inequality then they are the solution if the inequality

1) (1, -8)

`\begin{gathered} (1,-8)\text{ : x = 1 and y =-8} \\ \text{Substitute them in the inequality:} \\ x-4y<-12 \\ 1-4(-8)<-12 \\ 1+32<-12 \\ 33<-12 \\ \text{ Since -12 is not greater than 33, } \\ S\text{o the expression 33<-12 is wrong} \end{gathered}`

Hence, (1,-8) is not the solution of inequality : x - 4y < -12

2) (-8,-3)

`\begin{gathered} (-8,-3)\text{ : x = -8 and y =-}3 \\ \text{Substitute them in the inequality:} \\ x-4y<-12 \\ -8-4(-3)<-12 \\ -8+12<-12 \\ 4<-12 \\ \text{ Since -12 is not greater than 4, } \\ S\text{o the expression 4<-12 is wrong} \end{gathered}`

Hence, (-8, -3) is not the solution of inequality: x - 4y < -12

3) (-12,0)

`\begin{gathered} (-12,-0)\text{ : x = -12 and y =}0 \\ \text{Substitute them in the inequality:} \\ x-4y<-12 \\ -12-4(0)<-12 \\ -12<-12 \\ -<-12 \\ \text{ Since -12 is not greater than -12 they are equal, } \\ S\text{o the expression -12<-12 is wrong} \end{gathered}`

Hence, (-12,0) is not the solution of inequality : x - 4y <-12

4) (3,5)

`\begin{gathered} (3,5)\text{ : x = 3 and y =}5 \\ \text{Substitute them in the inequality:} \\ x-4y<-12 \\ 3-4(5)<-12 \\ 3-20<-12 \\ -17<-12 \\ \text{ Since -12 is greater than -17 } \\ S\text{o the expression -17<-12 is hold} \end{gathered}`

Hence, (3,5) is the solution of the inequality : x - 4y < -12

5) (-7, 9)

`\begin{gathered} (-7,9)\text{ : x = -7 and y =}9 \\ \text{Substitute them in the inequality:} \\ x-4y<-12 \\ -7-4(9)<-12 \\ -7-36<-12 \\ -43<-12 \\ \text{ Since -12 is greater than -43, } \\ S\text{o the expression -43<-12 is hold} \end{gathered}`

Hence, (-7,9) is the solution of the inequality : x - 4y < -12

6) (-4,2)

`\begin{gathered} (-4,2)\text{ : x = -4 and y =}2 \\ \text{Substitute them in the inequality:} \\ x-4y<-12 \\ -4-4(2)<-12 \\ -4-8<-12 \\ -12<-12 \\ \text{ Since -12 is not greater than -12, } \\ S\text{o the expression -12<-12 is wrong} \end{gathered}`

Hence, (-4,2) is not the solution of the inequality : x -4y <-12

Answer:

4) (3, 5)

5) (-7, 9)