Question

For each ordered pair, determine whether it is a solution to the system of equations. { 7x-4y=6 -6x+7y=2 (x, y) Is it a solution? Yes or no?
(6,9) (-8,0) (3, 3) (-5,-4)

Answer 1

To determine whether each ordered pair is a solution to the system of equations:

1. \(7x - 4y = 6\)
2. \(-6x + 7y = 2\)

we will substitute the values of \(x\) and \(y\) for each pair into both equations.

### Check each pair:

1. **For (6, 9):**
- Substitute into the first equation:
\[
7(6) - 4(9) = 42 - 36 = 6 \quad \text{(True)}
\]
- Substitute into the second equation:
\[
-6(6) + 7(9) = -36 + 63 = 27 \quad \text{(False)}
\]
- **Is it a solution? No**

2. **For (-8, 0):**
- Substitute into the first equation:
\[
7(-8) - 4(0) = -56 - 0 = -56 \quad \text{(False)}
\]
- **Is it a solution? No**

3. **For (3, 3):**
- Substitute into the first equation:
\[
7(3) - 4(3) = 21 - 12 = 9 \quad \text{(False)}
\]
- **Is it a solution? No**

4. **For (-5, -4):**
- Substitute into the first equation:
\[
7(-5) - 4(-4) = -35 + 16 = -19 \quad \text{(False)}
\]
- **Is it a solution? No**

### Summary of results:
- (6, 9): No
- (-8, 0): No
- (3, 3): No
- (-5, -4): No

None of the ordered pairs are solutions to the system of equations.

Answer 2

bro aint no way none of them dont got an answer

Answer 3

Let's reevaluate each ordered pair to check if any of them is a solution to the system of equations properly.

The system of equations is:
1. \( 7x - 4y = 6 \)
2. \( -6x + 7y = 2 \)

We will substitute each pair \((x, y)\) and check.

### Check each pair:

1. **For (6, 9):**
- Substitute into the first equation:
\[
7(6) - 4(9) = 42 - 36 = 6 \quad \text{(True)}
\]
- Substitute into the second equation:
\[
-6(6) + 7(9) = -36 + 63 = 27 \quad \text{(False)}
\]
- **Is it a solution?** **No**

2. **For (-8, 0):**
- Substitute into the first equation:
\[
7(-8) - 4(0) = -56 - 0 = -56 \quad \text{(False)}
\]
- **Is it a solution?** **No**

3. **For (3, 3):**
- Substitute into the first equation:
\[
7(3) - 4(3) = 21 - 12 = 9 \quad \text{(False)}
\]
- **Is it a solution?** **No**

4. **For (-5, -4):**
- Substitute into the first equation:
\[
7(-5) - 4(-4) = -35 + 16 = -19 \quad \text{(False)}
\]
- Substitute into the second equation:
\[
-6(-5) + 7(-4) = 30 - 28 = 2 \quad \text{(True)}
\]
- **Is it a solution?** **No** (it only works for the second equation)

Based on the checks, we confirm:
- (6, 9): No
- (-8, 0): No
- (3, 3): No
- (-5, -4): No

So, indeed, none of these pairs satisfy both equations simultaneously. If there’s a specific calculation you want me to explain or if you have other pairs, let me know!