Question

Which ordered pairs are solutions to the inequality 2y−x≤−6 ?

Select each correct answer.



(0, −3)

(2, −2)

(1, −4)

(6, 1)

(−3, 0)

Answer 1

try plugging them in, might seem tedious, but it's the best way to practice. if you plug in a pair and the left side of the equation is less than or equal to 6, it's the right answer.

Answer 2

we have

`2y-x\leq -6`

we know that

if a ordered pair is a solution of the inequality

then

the ordered pair must satisfy the inequality

we will proceed to verify each case to determine the solution of the problem

case A)
`(0,-3)`

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

`2*(-3)-0\leq -6`

`-6\leq -6` -------> Is True

therefore

the ordered pair
`(0,-3)` is a solution of the inequality

case B)
`(2,-2)`

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

`2*(-2)-2\leq -6`

`-6\leq -6` -------> Is True

therefore

the ordered pair
`(2,-2)` is a solution of the inequality

case C)
`(1,-4)`

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

`2*(-4)-1\leq -6`

`-9\leq -6` -------> Is True

therefore

the ordered pair
`(1,-4)` is a solution of the inequality

case D)
`(6,1)`

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

`2*(1)-6\leq -6`

`-4\leq -6` -------> Is False

therefore

the ordered pair
`(6,1)` is not a solution of the inequality

case E)
`(-3,0)`

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

`2*(0)-(-3)\leq -6`

`3\leq -6` -------> Is False

therefore

the ordered pair
`(-3,0)` is not a solution of the inequality

therefore

the answer is

`(0,-3)`

`(2,-2)`

`(1,-4)`