Question
Which of the following are solutions to 1.5x + 0.5y = 30
(2, 19)
(3, 31)
(13, 10)
(3.5, 19)
(5, 25)
(2, 19)
(3, 31)
(13, 10)
(3.5, 19)
(5, 25)
Answers
GPT-4o mini
To determine which of the given pairs \((x, y)\) are solutions to the equation \(1.5x + 0.5y = 30\), we can substitute the values of \(x\) and \(y\) from each pair into the equation and check if the equation is satisfied.
1. For \((2, 19)\):
\[
1.5(2) + 0.5(19) = 3 + 9.5 = 12.5 \quad (\text{not a solution})
\]
2. For \((3, 31)\):
\[
1.5(3) + 0.5(31) = 4.5 + 15.5 = 20 \quad (\text{not a solution})
\]
3. For \((13, 10)\):
\[
1.5(13) + 0.5(10) = 19.5 + 5 = 24.5 \quad (\text{not a solution})
\]
4. For \((3.5, 19)\):
\[
1.5(3.5) + 0.5(19) = 5.25 + 9.5 = 14.75 \quad (\text{not a solution})
\]
5. For \((5, 25)\):
\[
1.5(5) + 0.5(25) = 7.5 + 12.5 = 20 \quad (\text{not a solution})
\]
None of the given pairs \((2, 19)\), \((3, 31)\), \((13, 10)\), \((3.5, 19)\), or \((5, 25)\) solve the equation \(1.5x + 0.5y = 30\) based on the calculations above. Therefore, there are no solutions among the provided pairs.
1. For \((2, 19)\):
\[
1.5(2) + 0.5(19) = 3 + 9.5 = 12.5 \quad (\text{not a solution})
\]
2. For \((3, 31)\):
\[
1.5(3) + 0.5(31) = 4.5 + 15.5 = 20 \quad (\text{not a solution})
\]
3. For \((13, 10)\):
\[
1.5(13) + 0.5(10) = 19.5 + 5 = 24.5 \quad (\text{not a solution})
\]
4. For \((3.5, 19)\):
\[
1.5(3.5) + 0.5(19) = 5.25 + 9.5 = 14.75 \quad (\text{not a solution})
\]
5. For \((5, 25)\):
\[
1.5(5) + 0.5(25) = 7.5 + 12.5 = 20 \quad (\text{not a solution})
\]
None of the given pairs \((2, 19)\), \((3, 31)\), \((13, 10)\), \((3.5, 19)\), or \((5, 25)\) solve the equation \(1.5x + 0.5y = 30\) based on the calculations above. Therefore, there are no solutions among the provided pairs.