Question
Which ordered pairs in the form (x, y) are solutions to the equation 3x−4y=21?

Select each correct answer.

Responses

(−1, −6)
begin ordered pair negative 1 comma negative 6 end ordered pair

(−3, 3)
begin ordered pair negative 3 comma 3 end ordered pair

(11, 3)
Begin ordered pair 11 comma 3 end ordered pair

(7, 0)

We need to determine which ordered pairs \((x, y)\) are solutions to the equation \(3x - 4y = 21\). This can be done by substituting each pair of values into the equation and checking if the equation holds true.

1. **For \((-1, -6)\):**
   \[
   3(-1) - 4(-6) = -3 + 24 = 21
   \]
   This is **true**, so \((-1, -6)\) is a solution.

2. **For \((-3, 3)\):**
   \[
   3(-3) - 4(3) = -9 - 12 = -21
   \]
   This is **false**, so \((-3, 3)\) is not a solution.

3. **For \((11, 3)\):**
   \[
   3(11) - 4(3) = 33 - 12 = 21
   \]
   This is **true**, so \((11, 3)\) is a solution.

4. **For \((7, 0)\):**
   \[
   3(7) - 4(0) = 21 - 0 = 21
   \]
   This is **true**, so \((7, 0)\) is a solution.

### Correct solutions: 
\((-1, -6)\), \((11, 3)\), and \((7, 0)\).

Would you like more details or have any further questions?

Here are some related questions:
1. What is the general process for solving linear equations in two variables?
2. How can you determine the slope and intercept of the line \(3x - 4y = 21\)?
3. What does the graph of the equation \(3x - 4y = 21\) look like?
4. How can you verify if a point is a solution to a linear system of equations?
5. How do you solve systems of equations using substitution or elimination methods?

**Tip:** Always double-check by substituting values back into the equation to verify the solution.

Which ordered pairs in the form (x, y) are solutions to the equation 3x − 4y = 21?

Learn how to find which ordered pairs are solutions to the linear equation 3x - 4y = 21 using substitution. The step-by-step solution helps students verify answers through substitution and algebraic manipulation. Suitable for students in Grades 8-10.

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