Questions: Determine whether each ordered pair is a solution to the inequality (2 x-8 y geq 75). a. ((10,-7)) b. ((-11,-12)) c. ((7.5,-7.5)) a. Is the ordered pair ((10,-7)) a solution of the linear inequality? because substituting the (x)-and (y)-coordinates for the variables and simplifying on the left side results in which is to the right side

Determine whether each ordered pair is a solution to the inequality (2 x-8 y geq 75).
a. ((10,-7))
b. ((-11,-12))
c. ((7.5,-7.5))
a. Is the ordered pair ((10,-7)) a solution of the linear inequality?
because substituting the (x)-and (y)-coordinates for the variables and simplifying on the left side results in which is to the right side

Transcript text: Determine whether each ordered pair is a solution to the inequality $2 x-8 y \geq 75$. a. $(10,-7)$ b. $(-11,-12)$ c. $(7.5,-7.5)$ a. Is the ordered pair $(10,-7)$ a solution of the linear inequality? $\square$ because substituting the $x$-and $y$-coordinates for the variables and simplifying on the left side results in which is $\square$ to the right side

Solution

Solution Steps

To determine whether each ordered pair is a solution to the inequality $2x - 8y \geq 75$, we need to substitute the $x$ and $y$ values from each ordered pair into the inequality and check if the resulting expression is true.

Solution Approach

Substitute the $x$ and $y$ values from each ordered pair into the inequality $2x - 8y \geq 75$.
Simplify the left side of the inequality.
Compare the simplified left side to 75 to determine if the inequality holds.

Step 1: Substitute the Ordered Pair $(10, -7)$

Substituting $x = 10$ and $y = -7$ into the inequality: \[ 2(10) - 8(-7) = 20 + 56 = 76 \] Since $76 \geq 75$ is true, the ordered pair $(10, -7)$ is a solution.

Step 2: Substitute the Ordered Pair $(-11, -12)$

Substituting $x = -11$ and $y = -12$ into the inequality: \[ 2(-11) - 8(-12) = -22 + 96 = 74 \] Since $74 \geq 75$ is false, the ordered pair $(-11, -12)$ is not a solution.

Step 3: Substitute the Ordered Pair $(7.5, -7.5)$

Substituting $x = 7.5$ and $y = -7.5$ into the inequality: \[ 2(7.5) - 8(-7.5) = 15 + 60 = 75 \] Since $75 \geq 75$ is true, the ordered pair $(7.5, -7.5)$ is a solution.