Consider the system of inequalities below: \begin{aligned} 3x + y &> 5 \\ x - 2y &> 4 \end… — SAT

Consider the system of inequalities below:

\begin{aligned} 3x + y &> 5 \\ x - 2y &> 4 \end{aligned}

Which of the following coordinate pairs $(x, y)$ is a solution to the system?

(4, -2)

The coordinate pair

(4, -2)

is the correct answer because substituting these values into both inequalities of the system produces true statements:

3(4) + (-2) = 10 > 5

and

4 - 2(-2) = 8 > 4

Substitute the coordinates of the candidate point into the first inequality,

3x + y > 5

For

(4, -2)

, we get

3(4) + (-2) = 12 - 2 = 10

. Since

10 > 5

, the first inequality is satisfied.

A coordinate pair must satisfy both inequalities in the system to be a solution.

Substitute the coordinates of the candidate point into the second inequality,

x - 2y > 4

For

(4, -2)

, we get

4 - 2(-2) = 4 + 4 = 8

. Since

8 > 4

, the second inequality is also satisfied.

Since both inequalities are true for

(4, -2)

, it is a valid solution to the system.

A coordinate pair

(x, y)

is a solution to a system of linear inequalities if and only if it makes all inequalities in the system true when substituted.

Estimated Time:1m 30s

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