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 elimination or substitution method. Here, I'll use the elimination method.

First, let's eliminate \( y \) by adding both equations. To do that, we will first align the coefficients of \( y \).

From Equation 1, we can multiply it by \( 1 \) (no change):
\[
6x - 5y = 27
\]

From Equation 2, if we multiply it by \( 1 \) (no change as well):
\[
3x + 5y = 36
\]

Now we can add both equations:
\[
(6x - 5y) + (3x + 5y) = 27 + 36
\]
This simplifies to:
\[
9x = 63
\]
Dividing by \( 9 \):
\[
x = 7
\]

Now that we have \( x \), we can substitute it 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, isolate \( 5y \):
\[
5y = 36 - 21
\]
\[
5y = 15
\]
Dividing by \( 5 \):
\[
y = 3
\]

So the solution to the system of equations is:
\[
x = 7, \quad y = 3
\]

In ordered pair form, the solution is:
\[
(7, 3)
\]