Question

Solve each system by substitution.
1.) 6x - 4y = 54 , -9x + 2y - 69

Answer 1

To solve the system of equations using substitution, we'll first rewrite the equations clearly:

1) \( 6x - 4y = 54 \)
2) \( -9x + 2y = 69 \)

Let's solve the first equation for \( y \):

\[
6x - 4y = 54
\]

Rearranging for \( y \):

\[
-4y = 54 - 6x
\]

\[
y = \frac{6x - 54}{4}
\]

\[
y = \frac{3x - 27}{2}
\]

Now that we have \( y \) in terms of \( x \), we can substitute this expression for \( y \) into the second equation:

\[
-9x + 2y = 69
\]

Substituting \( y \):

\[
-9x + 2\left(\frac{3x - 27}{2}\right) = 69
\]

Multiply by 2 to eliminate the fraction:

\[
-9x + (3x - 27) = 69
\]

Combine like terms:

\[
-6x - 27 = 69
\]

Now, add 27 to both sides:

\[
-6x = 69 + 27
\]

\[
-6x = 96
\]

Divide by -6:

\[
x = -16
\]

Now, substitute \( x = -16 \) back into the expression we found for \( y \):

\[
y = \frac{3(-16) - 27}{2}
\]

\[
y = \frac{-48 - 27}{2}
\]

\[
y = \frac{-75}{2}
\]

\[
y = -37.5
\]

Thus, the solution to the system of equations is:

\[
x = -16, \quad y = -37.5
\]

So the final answer is:

\[
\boxed{(-16, -37.5)}
\]