Which of the following ordered pairs (x, y) is a solution to the system of inequalities be… — SAT

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

\begin{aligned} y &\geq 3x + 1 \\ y &< -2x + 5 \end{aligned}

(0, 2)

The ordered pair

(0, 2)

is correct because substituting these values into both inequalities results in true statements. Specifically,

2 \geq 3(0) + 1

becomes

2 \geq 1

, which is true, and

2 < -2(0) + 5

becomes

2 < 5

, which is also true.

Substitute the coordinates of the correct ordered pair into the first inequality,

y \geq 3x + 1

2 \geq 3(0) + 1 \Rightarrow 2 \geq 1

, which is true.

To be a solution to the system, an ordered pair must satisfy both inequalities in the system.

Substitute the coordinates of the same ordered pair into the second inequality,

y < -2x + 5

2 < -2(0) + 5 \Rightarrow 2 < 5

, which is true.

To verify the solution, we check if it satisfies the second constraint.

Testing coordinate solutions in a system of linear inequalities

Question