Question
Look at the linear equation.
(y−21)=3(x−15)
Which equation is a true solution for x
?
x=y−2
x=13(y−21)+15
x=3(y−15)+21
x=13(y−15)+21
(y−21)=3(x−15)
Which equation is a true solution for x
?
x=y−2
x=13(y−21)+15
x=3(y−15)+21
x=13(y−15)+21
Answers
Answered by
GPT-4o mini
To find which of the given equations is a true solution for \( x \) in the linear equation \( (y - 21) = 3(x - 15) \), we can start by rearranging this equation to solve for \( x \).
1. Start from the original equation:
\[
y - 21 = 3(x - 15)
\]
2. Expand the right side:
\[
y - 21 = 3x - 45
\]
3. Add 45 to both sides:
\[
y - 21 + 45 = 3x
\]
\[
y + 24 = 3x
\]
4. Divide by 3 to solve for \( x \):
\[
x = \frac{y + 24}{3}
\]
Now, let's analyze each option to see which one matches this equation:
1. **Option 1:** \( x = y - 2 \)
- This simplifies to \( 3x = 3(y - 2) = 3y - 6 \). This does not match \( 3x = y + 24 \).
2. **Option 2:** \( x = 13(y - 21) + 15 \)
- This simplifies to \( x = 13y - 273 + 15 = 13y - 258 \). This does not match either.
3. **Option 3:** \( x = 3(y - 15) + 21 \)
- This simplifies to \( x = 3y - 45 + 21 = 3y - 24 \). This does not match.
4. **Option 4:** \( x = 13(y - 15) + 21 \)
- This simplifies to \( x = 13y - 195 + 21 = 13y - 174 \). This also does not match.
None of the options provided match the result we derived (\( x = \frac{y + 24}{3} \)).
Upon reviewing, it appears there may be an error in the options provided, as none give a valid equation for \( x \) based on the transformation of the original linear equation. Please ensure that all options are correct or present alternative equations if possible.
1. Start from the original equation:
\[
y - 21 = 3(x - 15)
\]
2. Expand the right side:
\[
y - 21 = 3x - 45
\]
3. Add 45 to both sides:
\[
y - 21 + 45 = 3x
\]
\[
y + 24 = 3x
\]
4. Divide by 3 to solve for \( x \):
\[
x = \frac{y + 24}{3}
\]
Now, let's analyze each option to see which one matches this equation:
1. **Option 1:** \( x = y - 2 \)
- This simplifies to \( 3x = 3(y - 2) = 3y - 6 \). This does not match \( 3x = y + 24 \).
2. **Option 2:** \( x = 13(y - 21) + 15 \)
- This simplifies to \( x = 13y - 273 + 15 = 13y - 258 \). This does not match either.
3. **Option 3:** \( x = 3(y - 15) + 21 \)
- This simplifies to \( x = 3y - 45 + 21 = 3y - 24 \). This does not match.
4. **Option 4:** \( x = 13(y - 15) + 21 \)
- This simplifies to \( x = 13y - 195 + 21 = 13y - 174 \). This also does not match.
None of the options provided match the result we derived (\( x = \frac{y + 24}{3} \)).
Upon reviewing, it appears there may be an error in the options provided, as none give a valid equation for \( x \) based on the transformation of the original linear equation. Please ensure that all options are correct or present alternative equations if possible.