Question

is \\((-2,2)\\) a solution of the system \\(-4x + y \le 10\\) and \\(x + 4y \ge 6\\)

no
yes

Explanation:

Identify the given point and system

We are given the coordinate point \((-2, 2)\), where \(x = -2\) and \(y = 2\). We need to determine if this point satisfies the system of inequalities:

1. \(-4x + y \le 10\)
2. \(x + 4y \ge 6\)

Test the first inequality

Substitute \(x = -2\) and \(y = 2\) into the first inequality:

$$ -4(-2) + 2 \le 10 $$

Simplify the left side:

$$ 8 + 2 \le 10 \implies 10 \le 10 $$

Since \(10\) is equal to \(10\), this inequality is true.

Test the second inequality

Substitute \(x = -2\) and \(y = 2\) into the second inequality:

$$ -2 + 4(2) \ge 6 $$

Simplify the left side:

$$ -2 + 8 \ge 6 \implies 6 \ge 6 $$

Since \(6\) is equal to \(6\), this inequality is also true.

Determine the final solution status

Since the point \((-2, 2)\) satisfies both inequalities in the system, it is a valid solution to the system.

Answer:

• No
• Yes (Correct answer)