Question

solve the system of equations
6x + 5y = 27
3x + 5y = 36
(_,_)

Answer 1

To solve the system of equations:

1. \( 6x + 5y = 27 \) (Equation 1)
2. \( 3x + 5y = 36 \) (Equation 2)

We can use the elimination method or substitution method. Here, we will use the elimination method.

First, let's subtract Equation 2 from Equation 1 to eliminate \( y \):

\[
(6x + 5y) - (3x + 5y) = 27 - 36
\]

This simplifies to:

\[
6x - 3x + 5y - 5y = -9
\]

\[
3x = -9
\]

Now, divide by 3:

\[
x = -3
\]

Next, we substitute \( x = -3 \) back into one of the original equations to find \( y \). We'll use Equation 2:

\[
3(-3) + 5y = 36
\]

This simplifies to:

\[
-9 + 5y = 36
\]

Adding 9 to both sides gives:

\[
5y = 45
\]

Now, divide by 5:

\[
y = 9
\]

So, the solution to the system of equations is:

\[
(x, y) = (-3, 9)
\]

In ordered pair form, the solution is:

\[
\boxed{(-3, 9)}
\]