Question

Solve the system of equations.
6x–5y=27

3x+5y=36
(1 point)
(
,
)

Answer 1

To solve the system of equations:

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

We can use the method of substitution or elimination. Here, we'll use the elimination method.

First, let's add the two equations to eliminate \( y \):

- From Equation 1, we have:

\( 6x - 5y = 27 \)

- From Equation 2, we have:

\( 3x + 5y = 36 \)

Next, we can add these two equations together:

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

This simplifies to:

\[
6x + 3x = 63
\]

\[
9x = 63
\]

Now, divide both sides by 9:

\[
x = 7
\]

Next, we can substitute \( x = 7 \) back into one of the original equations to find \( y \). We'll use Equation 2:

\[
3(7) + 5y = 36
\]

This simplifies to:

\[
21 + 5y = 36
\]

Now, subtract 21 from both sides:

\[
5y = 15
\]

Dividing both sides by 5 gives:

\[
y = 3
\]

So the solution to the system of equations is:

\[
(x, y) = (7, 3)
\]

Thus, the solution is:

\[
\boxed{(7, 3)}
\]