To match each equation with its corresponding solutions, let's evaluate each equation and see which set of points satisfy them.
A. \( y = 1.5 \)
- This is a horizontal line where \( y \) remains \( 1.5 \) regardless of \( x \).
- Solutions: None of the points in the lists have \( y = 1.5 \), so this equation does not match any of these points.
B. \( 2x + 3y = 7 \)
- Rearranging gives \( y = \frac{7 - 2x}{3} \).
- Evaluate the given points:
- (14, 21): \( 2(14) + 3(21) = 28 + 63 = 91 \) (no)
- (2, 3): \( 2(2) + 3(3) = 4 + 9 = 13 \) (no)
- (8, -12): \( 2(8) + 3(-12) = 16 - 36 = -20 \) (no)
- Thus, this equation does not match with any set.
C. \( x - y = 4 \)
- Rearranging gives \( y = x - 4 \).
- Evaluate the given points:
- (-3,-7): \( -3 - (-7) = -3 + 7 = 4 \) (yes)
- (0,-4): \( 0 - (-4) = 0 + 4 = 4 \) (yes)
- (-1,-5): \( -1 - (-5) = -1 + 5 = 4 \) (yes)
- Therefore, matches with 2: (-3,-7), (0,-4), (-1,-5).
D. \( 3x = \frac{y}{2} \)
- Rearranging gives \( y = 6x \).
- Evaluate the given points:
- (1, 1.5): \( y = 6(1) = 6 \) (no)
- (-1, 3): \( y = 6(-1) = -6 \) (no)
- (0, 2.5): \( y = 6(0) = 0 \) (no)
- This equation does not match any set of points either.
E. \( y = -x + 1 \)
- Evaluate the given points:
- (0.5, 3): Did not satisfy
- (1, 6): Did not satisfy
- (1.2, 7.2): Did not satisfy
- Thus, this does match any set of points either.
Let's summarize the solutions again:
- A. Y=1.5 : No match
- B. 2x+3y=7: No match
- C. X-y=4 : Matches 2: (-3,-7), (0,-4), (-1,-5)
- D. 3x=y/2: No match
- E. Y=-x+1: No match
Therefore, the only matches we have are for C with set 2.
Here are the final matches:
- A: No match
- B: No match
- C: 2
- D: No match
- E: No match
Please let me know if you would like further assistance or another explanation!
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