Answer:
The system shown is consistent ⇒ A
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
- a = d, b = e, and c = f, then the system is consistent dependent and has infinitely many solutions
- a = d, b = e, and c ≠ f, then the system is inconsistent and has no solution
- a ≠ d, and/or b ≠ e, and/or c ≠ f, and [tex]\frac{a}{d}[/tex] ≠ [tex]\frac{b}{e}[/tex] , 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
