Question

9th grade math help me please pretty please

Answer 1

Answer:

The system has "infinitely many solutions; consistent and dependent" ⇒ 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

∵ r = -5s + 7

∵ r + 5s - 7 = 0

→ Put the equations in the form of equations above

∵ r = -5s + 7

→ Add -5s to both sides

∴ r + 5s = -5s + 5s + 7

∴ r + 5s = 7 ⇒ (1)

∵ r + 5s - 7 = 0

→ Add 7 to both sides

∴ r + 5s - 7 + 7 = 0 + 7

∴ r + 5s = 7

∴ r + 5s = 7 ⇒ (2)

→ By subtracting equations (1) and (2)

∵ (r - r) + (5s - 5s) = (7 - 7)

∴ 0 + 0 = 0

∴ 0 = 0

→ By using rule 1 above

∵ r = r

∵ 5s = 5s

∵ 7 = 7

∴ The system of equation is consistent dependent and has infinitely

   many solutions

∴ The system has "infinitely many solutions; consistent and dependent"