Graphing Linear Relationships

a

We can determine whether

(4, - 3)

is a solution by substituting it into the inequality and then simplify.

x + 2 y \geq - 6

SubstituteII

x = 4

,

y = - 3

4 + 2 (- 3) \geq ? - 6

MultPosNeg

a (- b) = - a \cdot b

4 - 6 \geq ? - 6

SubTermSubtract term

- 2 \geq - 6

Since

- 2

is greater than

- 6,

the ordered pair

(4, - 3)

is a solution. We can verify our conclusion by graphing the inequality and the point.

b

To determine whether

(4, - 3)

is a solution, we will substitute it into the inequality. If it produces a true statement, then the point is part of the solution set. If not, the point is not part of the solution set.

1 \leq - (x + y)

SubstituteII

x = - 1

,

y = - 1

1 \leq ? - (4 + (- 3))

RemoveParRemove parentheses

1 \leq ? - (4 - 3)

SubTermSubtract term

1 \leq ? - (1)

RemoveParSignsRemove parentheses and change signs

1 ≰ - 1

Since

1

is not less than or equal to

- 1,

the point

(4, - 3)

is a solution to the inequality. Let's verify this by graphing the inequality and the point.

Graphing Linear Relationships 1.8 - Solution