Question
Which of the following coordinates represent a solution to the equation 6x - 5y = 30?
The possible answers are:
(0,-5)
(0,-6)
(-5,0)
(-6,0)
The possible answers are:
(0,-5)
(0,-6)
(-5,0)
(-6,0)
Answers
Answered by
GPT-4o mini
To determine which of the given coordinates represent a solution to the equation \(6x - 5y = 30\), we will substitute each pair of coordinates \((x, y)\) into the equation and check if it holds true.
1. **For (0, -5):**
\[
6(0) - 5(-5) = 0 + 25 = 25 \quad (\text{Not a solution since } 25 \neq 30)
\]
2. **For (0, -6):**
\[
6(0) - 5(-6) = 0 + 30 = 30 \quad (\text{This is a solution since } 30 = 30)
\]
3. **For (-5, 0):**
\[
6(-5) - 5(0) = -30 - 0 = -30 \quad (\text{Not a solution since } -30 \neq 30)
\]
4. **For (-6, 0):**
\[
6(-6) - 5(0) = -36 - 0 = -36 \quad (\text{Not a solution since } -36 \neq 30)
\]
From this analysis, the only coordinate that represents a solution to the equation \(6x - 5y = 30\) is \((0, -6)\).
1. **For (0, -5):**
\[
6(0) - 5(-5) = 0 + 25 = 25 \quad (\text{Not a solution since } 25 \neq 30)
\]
2. **For (0, -6):**
\[
6(0) - 5(-6) = 0 + 30 = 30 \quad (\text{This is a solution since } 30 = 30)
\]
3. **For (-5, 0):**
\[
6(-5) - 5(0) = -30 - 0 = -30 \quad (\text{Not a solution since } -30 \neq 30)
\]
4. **For (-6, 0):**
\[
6(-6) - 5(0) = -36 - 0 = -36 \quad (\text{Not a solution since } -36 \neq 30)
\]
From this analysis, the only coordinate that represents a solution to the equation \(6x - 5y = 30\) is \((0, -6)\).