Question

For each ordered pair, determine whether it is a solution to the system of equations.
3x- 2y=7
Y=2x-1
(x, y)
Is it a solution?
Yes
No
(1, - 2)


(4,7)


(-5, - 11)


(0, 6)

Answer 1

To determine if the given ordered pairs are solutions to the system of equations, we need to substitute each pair into both equations:

1. **Equations**:
- \(3x - 2y = 7\)
- \(y = 2x - 1\)

2. **Ordered Pairs**:
- \((1, -2)\)
- \((4, 7)\)
- \((-5, -11)\)
- \((0, 6)\)

Now, let's check each pair one by one:

### 1. For **(1, -2)**:
- Substitute \(x = 1\) and \(y = -2\) into the first equation:
\[
3(1) - 2(-2) = 3 + 4 = 7 \quad \text{(True)}
\]
- Substitute into the second equation:
\[
-2 = 2(1) - 1 = 2 - 1 = 1 \quad \text{(False)}
\]
- **Not a solution**.

### 2. For **(4, 7)**:
- Substitute \(x = 4\) and \(y = 7\) into the first equation:
\[
3(4) - 2(7) = 12 - 14 = -2 \quad \text{(False)}
\]
- **Not a solution**.

### 3. For **(-5, -11)**:
- Substitute \(x = -5\) and \(y = -11\) into the first equation:
\[
3(-5) - 2(-11) = -15 + 22 = 7 \quad \text{(True)}
\]
- Substitute into the second equation:
\[
-11 = 2(-5) - 1 = -10 - 1 = -11 \quad \text{(True)}
\]
- **Is a solution**.

### 4. For **(0, 6)**:
- Substitute \(x = 0\) and \(y = 6\) into the first equation:
\[
3(0) - 2(6) = 0 - 12 = -12 \quad \text{(False)}
\]
- **Not a solution**.

### Summary:
- (1, -2): **No**
- (4, 7): **No**
- (-5, -11): **Yes**
- (0, 6): **No**