Match the system of equations with the ordered pair that is a solution to the system (−6, 0) (0, −6) (6, 0) y = 1/3x + 2 y = −2/3x − 4 y = −2x + 12 y = −5/6x + 5 y = −5x − 6 y = −1/3x − 6

To find which ordered pair is a solution to the system of equations, we can substitute each ordered pair into the equations and see which ones satisfy.

1. For the pair (-6, 0):

– Check each equation:

– ( y = frac{1}{3}(-6) + 2 Rightarrow 0 = -2 + 2 Rightarrow 0 = 0 ) (True)

– The pair (-6, 0) satisfies the first equation.

2. For the pair (0, -6):

– Check each equation:

– ( y = frac{1}{3}(0) + 2 Rightarrow -6 = 2 ) (False)

– It does not satisfy the first equation.

3. For the pair (6, 0):

– Check each equation:

– ( y = frac{1}{3}(6) + 2 Rightarrow 0 = 2 + 2 Rightarrow 0 = 4 ) (False)

– It does not satisfy the first equation.

So the ordered pair that is a solution to the system is (-6, 0) for the equation ( y = frac{1}{3}x + 2 ).

You can check other equations similarly if needed, but from this analysis, this pair works for the first equation.

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