Question

9th grade math help me please and thank you sosomuch

Answer 1

The system is consistent; it has one solution ⇒ D

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