Question

Match each equation with its three solutions
A. Y=1.5
B. 2x+3y=7
C. X-y=4
D. 3x=y/2
E. Y=-x+1
1. (14,21),(2,3),(8,!2)
2. (-3,-7),(0,-4),(-1,-5)
3.(1/8,7/8),(1/2,1/2),(1/4,3/4)
4.(1,1 2/3),(-1,3),(0,2 1/3)
5.(0.5,3),(1,6),(1.2,7.2)

Answer 1

To match each equation with its corresponding solutions, we need to evaluate the equations and check which solutions satisfy them.

**A. Y = 1.5**
This equation is a horizontal line where y always equals 1.5. Thus, all points with a y-coordinate of 1.5 will be solutions. There are no pairs listed directly showing this.

---

**B. 2x + 3y = 7**
We can plug in the solutions to see which satisfy:

1. (14, 21): 2(14) + 3(21) = 28 + 63 = 91 (not a solution)
2. (2, 3): 2(2) + 3(3) = 4 + 9 = 13 (not a solution)
3. (1/8, 7/8): 2(1/8) + 3(7/8) = 1/4 + 21/8 = 1/4 + 2.625 = 2.875 (not a solution)
4. (1, 1 2/3): 2(1) + 3(5/3) = 2 + 5 = 7 (is a solution)
5. (0.5, 3): 2(0.5) + 3(3) = 1 + 9 = 10 (not a solution)

From the above analysis, (-3,-7) does not satisfy. Thus, this one likely leads to (-1, 5), (0, 7).

---

**C. X - y = 4**
1. (14, 21): 14 - 21 = -7 (not a solution)
2. (-3, -7): -3 - (-7) = 4 (is a solution)
3. (1/8, 7/8): 1/8 - 7/8 = -3/4 (not a solution)
4. (1, 1 2/3): 1 - (5/3) = -2/3 (not a solution)
5. (0.5, 3): 0.5 - 3 = -2.5 (not a solution)

From this analysis, only (-3, -7) fits.

---

**D. 3x = y/2**
1. (14, 21): 3(14) = 42 and 21/2 = 10.5 (not a solution)
2. (-3, -7): 3(-3) = -9 and (-7/2) = -3.5 (not a solution)
3. (1/8, 7/8): 3(1/8) = 3/8 and (7/8)/2 = 7/16 (not a solution)
4. (1, 1 2/3): 3(1) = 3 and (5/3)/2 = 5/6 (not a solution)
5. (0.5, 3): 3(0.5) = 1.5 and (3/2) = 1.5 (is a solution)

---

**E. Y = -x + 1**
Let’s find solutions for this equation:
1. (14, 21): 21 != -14 + 1 (not a solution)
2. (-3, -7): -7 != -(-3) + 1 (not a solution)
3. (1/8, 7/8): 7/8 != -(1/8) + 1 (not a solution)
4. (1, 1 2/3): 1 2/3 is not equal to -1 + 1 (not a solution)
5. (0.5, 3): 3 != -(0.5) + (1) (not a solution)

To summarize:
- B fits (-1, 5),(0,2),(1,3)
- C fits (4, 1) and so forth.

The correct answers are:
- A: none match
- B: (1,1 2/3),(-1,3),(0,2 1/3)
- C: -3,-7 fits
- D: 0.5, 3 fits, also giving a too complete ratchet.

Ultimately:
1. A: None (1.5 is independent)
2. B: 2 + 3
3. C: Complete pairing
4. D: 0.5, 3

I suggest re-evaluating for accurate identification. Consider creating a system as above.