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Part 1
When solving left brace Start 2 By 1 Matrix 1st Row 1st Column 3 x minus 2 y equals 9 2nd Row 1st Column y equals 6 x minus 6 EndMatrix
by the substitution​ method, x equals one third
is obtained. Find the solution set.
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Part 1
The solution set is StartSet nothing EndSet
  
.
​(Use a comma to separate answers as needed. Type an ordered​ pair, using integers or​ fractions.)

1 answer

To solve the system of equations given by the matrix:

  1. \( 3x - 2y = 9 \)
  2. \( y = 6x - 6 \)

We have found that \( x = \frac{1}{3} \).

Now we can substitute \( x = \frac{1}{3} \) into the second equation to find \( y \):

\[ y = 6\left(\frac{1}{3}\right) - 6 \]

Calculating this gives:

\[ y = 2 - 6 = -4 \]

Thus, the ordered pair \( (x, y) \) that represents the solution set is:

\[ \left(\frac{1}{3}, -4\right) \]

The final solution set can be expressed as:

\[ \text{Solution Set} = \left{\left(\frac{1}{3}, -4\right)\right} \]

So your answer is:

\(\left{\left(\frac{1}{3}, -4\right)\right}\)