Question

For each ordered pair, determine whether it is a solution to the system of equations.

3x-2y=-9
2x+5y=-6
(x, y)
Is it a solution?
Yes
No
(-3, 0)


(-5, -3)


(7, -4)


(6, 2)

Answer 1

To determine whether each ordered pair is a solution to the system of equations, we'll substitute \(x\) and \(y\) values from each pair into both equations and check if they hold true. The system of equations is:

1. \(3x - 2y = -9\)
2. \(2x + 5y = -6\)

Let's evaluate each pair:

### Pair 1: \((-3, 0)\)

Substituting \(x = -3\) and \(y = 0\):

**For the first equation:**
\[
3(-3) - 2(0) = -9 \implies -9 = -9 \quad \text{(True)}
\]

**For the second equation:**
\[
2(-3) + 5(0) = -6 \implies -6 = -6 \quad \text{(True)}
\]

**Conclusion:** Yes, \((-3, 0)\) is a solution.

---

### Pair 2: \((-5, -3)\)

Substituting \(x = -5\) and \(y = -3\):

**For the first equation:**
\[
3(-5) - 2(-3) = -9 \implies -15 + 6 = -9 \implies -9 = -9 \quad \text{(True)}
\]

**For the second equation:**
\[
2(-5) + 5(-3) = -6 \implies -10 - 15 = -6 \implies -25 \neq -6 \quad \text{(False)}
\]

**Conclusion:** No, \((-5, -3)\) is not a solution.

---

### Pair 3: \((7, -4)\)

Substituting \(x = 7\) and \(y = -4\):

**For the first equation:**
\[
3(7) - 2(-4) = -9 \implies 21 + 8 = -9 \implies 29 \neq -9 \quad \text{(False)}
\]

**For the second equation:**
\[
2(7) + 5(-4) = -6 \implies 14 - 20 = -6 \implies -6 = -6 \quad \text{(True)}
\]

**Conclusion:** No, \((7, -4)\) is not a solution.

---

### Pair 4: \((6, 2)\)

Substituting \(x = 6\) and \(y = 2\):

**For the first equation:**
\[
3(6) - 2(2) = -9 \implies 18 - 4 = -9 \implies 14 \neq -9 \quad \text{(False)}
\]

**For the second equation:**
\[
2(6) + 5(2) = -6 \implies 12 + 10 = -6 \implies 22 \neq -6 \quad \text{(False)}
\]

**Conclusion:** No, \((6, 2)\) is not a solution.

---

### Summary of Results:

1. \((-3, 0)\): Yes
2. \((-5, -3)\): No
3. \((7, -4)\): No
4. \((6, 2)\): No