Question

Question
Solve the system of equations.
3x+6y=21

–5x+2y=13
(1 point)
(
,
)

Answer 1

To solve the system of equations

1) \( 3x + 6y = 21 \)
2) \( -5x + 2y = 13 \)

we can use either the substitution method or the elimination method. Here, I'll use the elimination method for clarity.

First, simplify the first equation:

\[
3x + 6y = 21
\]

Dividing the entire equation by 3:

\[
x + 2y = 7 \quad \text{(Equation 1)}
\]

So, we have two simplified equations:

1) \( x + 2y = 7 \)
2) \( -5x + 2y = 13 \)

Next, let's eliminate \( y \) by subtracting the first equation from the second equation:

\[
(-5x + 2y) - (x + 2y) = 13 - 7
\]

Simplifying:

\[
-5x + 2y - x - 2y = 6
\]

This reduces to:

\[
-6x = 6
\]

Dividing both sides by -6 gives:

\[
x = -1
\]

Now, we can substitute \( x = -1 \) back into Equation 1 to find \( y \):

\[
-1 + 2y = 7
\]

Adding 1 to both sides:

\[
2y = 8
\]

Dividing by 2:

\[
y = 4
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-1, 4)
\]

We can summarize the answer as:

\[
\boxed{(-1, 4)}
\]