Question

The system shown is _____.

A.) consistent
B.) inconsistent
C.) equivalent

Answer 1

The system shown is consistent ⇒ A

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, and
   `(a)/(d)` ≠
   `(b)/(e)` , then the system is consistent independent and has exactly one solution

From the given graph

∵ The two lines intersected at one point

∴ This point lies on the two lines

→ That means this point satisfies the equations of the lines

∴ The system of equations represented by the two lines has 1 solution

→ By using rule 3 above

∴ The system shown is consistent