Question

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.
Question content area bottom
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.)

Answer 1

To solve the system of equations using the substitution method, we start with the given equations:

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

You've obtained \(x = \frac{1}{3}\). Now we can find the corresponding \(y\) value using the second equation.

Substituting \(x = \frac{1}{3}\) into the second equation:

\[
y = 6\left(\frac{1}{3}\right) - 6
\]
\[
y = 2 - 6
\]
\[
y = -4
\]

Now that we have both \(x\) and \(y\), the solution is:

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

Thus, the solution set is:

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

In ordered pair notation, this is:

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