Math  /  Algebra

QuestionIs (2,8)(2,8) a solution to this system of inequalities? yx+6y7\begin{array}{l} y \geq x+6 \\ y \geq 7 \end{array} yes no

Studdy Solution

STEP 1

1. We are given a system of inequalities.
2. We need to check if the point (2,8)(2, 8) satisfies both inequalities.
3. A point (x,y)(x, y) is a solution if it makes all inequalities true.

STEP 2

1. Substitute the point into the first inequality and check.
2. Substitute the point into the second inequality and check.
3. Determine if the point satisfies both inequalities.

STEP 3

Substitute the point (2,8)(2, 8) into the first inequality yx+6y \geq x + 6.
82+6 8 \geq 2 + 6
Calculate the right-hand side:
88 8 \geq 8
This inequality is true.

STEP 4

Substitute the point (2,8)(2, 8) into the second inequality y7y \geq 7.
87 8 \geq 7
This inequality is also true.

STEP 5

Since the point (2,8)(2, 8) satisfies both inequalities, it is a solution to the system.
The answer is yes\boxed{\text{yes}}.

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