Question

In Exercises 3–8, tell whether the ordered pair is
a solution of the system of linear inequalities.
(See Example 1.)
3. (1, 2);
y ≥ 5x − 6
y ≤ 3x + 1
y > −x + 2


6.(−2, 5);
y ≤ x + 3
y ≥ −x
3x − y > −6

please easy

Answer 1

To determine whether the ordered pairs are solutions to the given systems of linear inequalities, we will substitute the \(x\) and \(y\) values of the ordered pairs into each inequality and see if they satisfy all conditions.

### Exercise 3: Ordered Pair (1, 2)

1. **Inequality:** \(y \geq 5x - 6\)
- Substitute \(x = 1\) and \(y = 2\):
\[ 2 \geq 5(1) - 6 \]
\[ 2 \geq 5 - 6 \]
\[ 2 \geq -1 \] (True)

2. **Inequality:** \(y \leq 3x + 1\)
- Substitute \(x = 1\) and \(y = 2\):
\[ 2 \leq 3(1) + 1 \]
\[ 2 \leq 3 + 1 \]
\[ 2 \leq 4 \] (True)

3. **Inequality:** \(y > -x + 2\)
- Substitute \(x = 1\) and \(y = 2\):
\[ 2 > -1 + 2 \]
\[ 2 > 1 \] (True)

Since the ordered pair (1, 2) satisfies all three inequalities, **it is a solution** to the system of inequalities.

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### Exercise 6: Ordered Pair (-2, 5)

1. **Inequality:** \(y \leq x + 3\)
- Substitute \(x = -2\) and \(y = 5\):
\[ 5 \leq -2 + 3 \]
\[ 5 \leq 1 \] (False)

Since the first inequality is false, there's no need to check the other inequalities. The ordered pair (-2, 5) **is not a solution** to this system of inequalities.

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### Summary
- **Exercise 3:** (1, 2) is a solution.
- **Exercise 6:** (-2, 5) is not a solution.