Which point satisfies the equation `3x - 4y = 7?`

Options

A. `(-5,2)`
B. `(5,2)`
C. `(3,-4)`
D. `(7,2)`

Answer

To determine which point satisfies the equation \(3x - 4y = 7\), we will substitute the coordinates of each point into the equation and check if the left-hand side (LHS) equals the right-hand side (RHS).

### Step-by-Step Solution:

1. **Identify the equation**: We have the equation \(3x - 4y = 7\).

2. **Choose a point to test**: Let's start with the first point, \((-5, 2)\).
- Here, \(x = -5\) and \(y = 2\).

3. **Substitute the values into the equation**:
\[ 3(-5) - 4(2) = 7 \]
- Calculate \(3(-5)\):
\[ -15 \]
- Calculate \(-4(2)\):
\[ -8 \]
- Now combine these results:
\[ -15 - 8 = -23 \]

4. **Check if LHS equals RHS**:
\[ -23 \neq 7 \]
- This means the point \((-5, 2)\) does not satisfy the equation.

5. **Choose the next point to test**: Now, let's test the point \((5, 2)\).
- Here, \(x = 5\) and \(y = 2\).

6. **Substitute the values into the equation**:
\[ 3(5) - 4(2) = 7 \]
- Calculate \(3(5)\):
\[ 15 \]
- Calculate \(-4(2)\):
\[ -8 \]
- Now combine these results:
\[ 15 - 8 = 7 \]

7. **Check if LHS equals RHS**:
\[ 7 = 7 \]
- This means the point \((5, 2)\) satisfies the equation.

### Conclusion:
The point that satisfies the equation \(3x - 4y = 7\) is \((5, 2)\).

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