which ordered pair is a solution of the equation 2x+3y=-7

To find which ordered pair \((x, y)\) is a solution to the equation \(2x + 3y = -7\), we substitute different values of \(x\) and \(y\) into the equation to see if the equation holds true.

Let's try a few examples:

1. **Ordered pair**: \((1, -3)\)
   \[
   2(1) + 3(-3) = 2 - 9 = -7
   \]
   This pair is a solution because it satisfies the equation.

2. **Ordered pair**: \((0, -\frac{7}{3})\)
   \[
   2(0) + 3\left(-\frac{7}{3}\right) = 0 - 7 = -7
   \]
   This pair is also a solution.

3. **Ordered pair**: \((2, 1)\)
   \[
   2(2) + 3(1) = 4 + 3 = 7
   \]
   This pair is **not** a solution because the result is \(7\), not \(-7\).

4. **Ordered pair**: \((-2, 1)\)
   \[
   2(-2) + 3(1) = -4 + 3 = -1
   \]
   This pair is **not** a solution because the result is \(-1\), not \(-7\).

5. **Ordered pair**: \((3, -\frac{13}{3})\)
   \[
   2(3) + 3\left(-\frac{13}{3}\right) = 6 - 13 = -7
   \]
   This pair is a solution.

So, the ordered pairs \((1, -3)\), \((0, -\frac{7}{3})\), and \((3, -\frac{13}{3})\) are solutions to the equation.

Do you want more details, or do you have any questions?

### Related Questions:
1. How do you find the solution of a system of linear equations?
2. What are the methods to solve linear equations?
3. How can you graph the equation \(2x + 3y = -7\)?
4. What is the significance of the slope and intercept in linear equations?
5. How do you determine if a point lies on the graph of a linear equation?

### Tip:
When testing if an ordered pair is a solution to an equation, substitute the values of \(x\) and \(y\) directly into the equation to see if both sides are equal.

Explore which ordered pairs \((x, y)\) satisfy the equation 2x + 3y = -7 through detailed substitution examples. Understand the concept of solutions in linear equations and practice identifying valid solutions. Suitable for students in Grades 7-9.

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