Question

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

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

$(0,-3)$

$(2,-2)$

$(1,-4)$