Question

Which of the following ordered pairs is a solution to 2.5y−3x=10 ?(1 point)
Responses

(−5,−2)
left parenthesis negative 5 comma negative 2 right parenthesis

(5,2)
left parenthesis 5 comma 2 right parenthesis

(5,−2)
left parenthesis 5 comma negative 2 right parenthesis

(−5,2)

Answer 1

To determine which ordered pair is a solution to the equation \(2.5y - 3x = 10\), we can substitute each pair into the equation and check if it holds true.

1. For \((-5, -2)\):
\[
2.5(-2) - 3(-5) = -5 + 15 = 10 \quad \text{(True)}
\]

2. For \((5, 2)\):
\[
2.5(2) - 3(5) = 5 - 15 = -10 \quad \text{(False)}
\]

3. For \((5, -2)\):
\[
2.5(-2) - 3(5) = -5 - 15 = -20 \quad \text{(False)}
\]

4. For \((-5, 2)\):
\[
2.5(2) - 3(-5) = 5 + 15 = 20 \quad \text{(False)}
\]

The only ordered pair that satisfies the equation is \((-5, -2)\).

Thus, the solution to \(2.5y - 3x = 10\) is:

**\((-5, -2)\)**

Answer 2

step by step how?

Answer 3

Sure! Let's go through the process step by step to determine which ordered pair is a solution to the equation \(2.5y - 3x = 10\).

**Step 1: Understand the equation**
We need to test each ordered pair (x, y) in the equation \(2.5y - 3x = 10\) to see if it satisfies the equation.

**Step 2: Substitute each ordered pair into the equation**

We will test each pair one by one.

### Testing \((-5, -2)\)

1. **Identify x and y:**
- \(x = -5\)
- \(y = -2\)

2. **Substitute into the equation:**
\[
2.5(-2) - 3(-5)
\]
\[
= -5 + 15
\]
\[
= 10
\]

3. **Check if it equals 10:**
\[
10 = 10 \quad \text{(True)}
\]

### Testing \((5, 2)\)

1. **Identify x and y:**
- \(x = 5\)
- \(y = 2\)

2. **Substitute into the equation:**
\[
2.5(2) - 3(5)
\]
\[
= 5 - 15
\]
\[
= -10
\]

3. **Check if it equals 10:**
\[
-10 \neq 10 \quad \text{(False)}
\]

### Testing \((5, -2)\)

1. **Identify x and y:**
- \(x = 5\)
- \(y = -2\)

2. **Substitute into the equation:**
\[
2.5(-2) - 3(5)
\]
\[
= -5 - 15
\]
\[
= -20
\]

3. **Check if it equals 10:**
\[
-20 \neq 10 \quad \text{(False)}
\]

### Testing \((-5, 2)\)

1. **Identify x and y:**
- \(x = -5\)
- \(y = 2\)

2. **Substitute into the equation:**
\[
2.5(2) - 3(-5)
\]
\[
= 5 + 15
\]
\[
= 20
\]

3. **Check if it equals 10:**
\[
20 \neq 10 \quad \text{(False)}
\]

**Step 3: Summarize findings**
- The only ordered pair that satisfies the equation \(2.5y - 3x = 10\) is \((-5, -2)\).

Therefore, the solution is:

**\((-5, -2)\)**.