Answer: Equivalent
Step-by-step explanation:
[tex]y=-\dfrac{1}{3}x+\dfrac{2}{3}\\\\\text{Multiply by 3 to clear the denominator: }3y = -x + 2\\\text{Add x to both sides: }x+3y=2\\\text{Multiply both sides by 2: }2x+6y=4[/tex]
When given a system of equations, the definitions of the solution are:
- Consistent & Independent: exactly ONE solution (lines intersect)
- Consistent & Dependent: INFINITE solutions (same line)
- Inconsistent: NO solutions (parallel lines)
In the given system, the equations are the same which means they have INFINITE solutions --> The system is Consistent & Dependent = Equivalent.
