Which point would be a solution to the system of linear inequalities shown below?
y, is less than, 3, x, plus, 8, y, is greater than, minus, 2, x, plus, 3
y<3x+8y>−2x+3
Answer
Multiple Choice Answers
left parenthesis, minus, 6, comma, 0, right parenthesis(−6,0)
left parenthesis, minus, 12, comma, minus, 10, right parenthesis(−12,−10)
left parenthesis, minus, 12, comma, 4, right parenthesis(−12,4)
left parenthesis, 4, comma, 10, right parenthesis(4,10)

To determine which point is a solution to the system of inequalities:

\[
y < 3x + 8 \quad \text{and} \quad y > -2x + 3
\]

we will test each of the given points by substituting the coordinates \((x, y)\) into both inequalities and check if both inequalities are satisfied.

### 1. Point \((-6, 0)\)

- For \(y < 3x + 8\):
  \[
  0 < 3(-6) + 8 = -18 + 8 = -10
  \]
  This is **false** because \(0 \not< -10\).

### 2. Point \((-12, -10)\)

- For \(y < 3x + 8\):
  \[
  -10 < 3(-12) + 8 = -36 + 8 = -28
  \]
  This is **false** because \(-10 \not< -28\).

### 3. Point \((-12, 4)\)

- For \(y < 3x + 8\):
  \[
  4 < 3(-12) + 8 = -36 + 8 = -28
  \]
  This is **false** because \(4 \not< -28\).

### 4. Point \((4, 10)\)

- For \(y < 3x + 8\):
  \[
  10 < 3(4) + 8 = 12 + 8 = 20
  \]
  This is **true** because \(10 < 20\).

- For \(y > -2x + 3\):
  \[
  10 > -2(4) + 3 = -8 + 3 = -5
  \]
  This is **true** because \(10 > -5\).

### Conclusion:
The point \((4, 10)\) satisfies both inequalities, so it is the solution.

### Answer: \((4, 10)\)

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Do you want further details on any part of this solution, or have any questions?

Here are 5 related questions:
1. How do you graph the system of inequalities \(y < 3x + 8\) and \(y > -2x + 3\)?
2. Can a system of inequalities have more than one solution?
3. How would the solution region of this system change if the inequalities were non-strict (i.e., \( \leq \) and \( \geq \))?
4. How do you solve a system of inequalities with more than two constraints?
5. Can the method used here apply to nonlinear inequalities?

**Tip:** Always graph the system of inequalities to visualize the solution set clearly.

Which point would be a solution to the system of linear inequalities shown below? y < 3x + 8 and y > -2x + 3.

Learn how to determine which point satisfies the system of linear inequalities y < 3x + 8 and y > -2x + 3. This step-by-step solution covers key concepts in linear inequalities and graphing. Suitable for students in Grades 9-10.

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