Question

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

3x+5y=36
(1 poi

Answer 1

To solve the system of equations:

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

We can use the method of substitution or elimination. Here, let's use the elimination method:

First, let's eliminate \(y\) by adding the two equations. To do this, we will first manipulate the equations to align the coefficients of \(y\).

Notice that if we multiply Equation 2 by \(1\) (to keep it as is), we can directly add the two equations since the coefficient of \(y\) in Equation 1 is \(-5\) while it is \(+5\) in Equation 2.

Starting with the two equations:
\[
6x - 5y = 27 \quad \text{(Equation 1)}
\]
\[
3x + 5y = 36 \quad \text{(Equation 2)}
\]

Now, we'll add both equations together:
\[
(6x - 5y) + (3x + 5y) = 27 + 36
\]
This simplifies to:
\[
9x = 63
\]
Now, divide both sides by 9:
\[
x = 7
\]

Now that we have \(x\), we can substitute this value back into either of the original equations to find \(y\). Let's use Equation 2:
\[
3(7) + 5y = 36
\]
This simplifies to:
\[
21 + 5y = 36
\]
Subtracting 21 from both sides:
\[
5y = 15
\]
Now, divide by 5:
\[
y = 3
\]

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

In conclusion, the solution to the system is:
\((x, y) = (7, 3)\).