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Sveta_85 [38]
3 years ago
12

A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one-quarter of the seco

nd number and 5. The situation can be represented by using the graph below, where x represents the second number.
Which equations represent the situation?
y=1/2x+3 and y=1/4x+5
y=3x+1/2 and y=5x+1/4
y=2x+3 and y=4x+5
y=3x+2 and y=5x+4
Mathematics
2 answers:
Brrunno [24]3 years ago
6 0
Y=1/2+3 And y=1/4+5 hope this helps
vfiekz [6]3 years ago
3 0
The first one is correct so A
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Answer:

The system is consistent; it has one solution ⇒ D

Step-by-step explanation:

A consistent system of equations has at least one solution

  • The consistent independent system has exactly 1 solution
  • The consistent dependent system has infinitely many solutions

An inconsistent system has no solution

In the system of equations ax + by = c and dx + ey = f, if

  1. a = d, b = e, and c = f, then the system is consistent dependent and has infinitely many solutions
  2. a = d, b = e, and c ≠ f, then the system is inconsistent and has no solution
  3. a ≠ d, and/or b ≠ e, and/or c ≠ f, then the system is consistent independent and has exactly one solution

In the given system of equations

∵ -2y + 2x = 3 ⇒ (1)

∵ -5y + 5x = 12 ⇒ (2)

→ By comparing equations (1) and (2)

∵ -2 ≠ -5

∵ 2 ≠ 5

∵ 3 ≠ 12

→ By using the 3rd rule above

∴ The system is consistent independent and has exactly one solution

∴ The system is consistent; it has one solution

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