Consider the system of inequalities shown below: \begin{aligned} y &\geq 2x + 1 \\ y &< -x… — SAT

Consider the system of inequalities shown below:

\begin{aligned} y &\geq 2x + 1 \\ y &< -x + 6 \end{aligned}

Which coordinate pair $(x, y)$ is a solution to the system?

The coordinate pair

(1, 4)

is a solution to the system of inequalities.

The coordinate pair

(1, 4)

is the correct answer because substituting

x = 1

and

y = 4

into both inequalities yields true statements:

4 \geq 2(1) + 1 \Rightarrow 4 \geq 3

is true, and

4 < -1 + 6 \Rightarrow 4 < 5

is true.

Substitute the coordinates of the correct pair,

(1, 4)

, into the first inequality,

y \geq 2x + 1

4 \geq 2(1) + 1 \Rightarrow 4 \geq 3

, which is true.

To be a solution to the system, the point must satisfy the first inequality.

Substitute the same coordinates,

(1, 4)

, into the second inequality,

y < -x + 6

4 < -1 + 6 \Rightarrow 4 < 5

, which is true.

The point must also satisfy the second inequality to be a solution to the entire system.

Conclude that since

(1, 4)

satisfies both inequalities, it is a solution to the system.

The point

(1, 4)

is in the solution set.

A coordinate pair is a solution to a system of inequalities if and only if it satisfies every inequality in the system.

Testing coordinate pairs in a system of linear inequalities by substitution.

Estimated Time:45s

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