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 the substitution or elimination method. Here, we'll use the substitution method by first solving the first equation for \( y \).

Starting with the first equation:

1. \( 3x + 6y = 21 \)

We can simplify this equation by dividing all terms by 3:

\[
x + 2y = 7
\]

Now, we can solve for \( y \):

\[
2y = 7 - x
\]
\[
y = \frac{7 - x}{2}
\]

Next, we will substitute this expression for \( y \) into the second equation:

2. \( -5x + 2y = 13 \)

Substituting \( y \):

\[
-5x + 2\left(\frac{7 - x}{2}\right) = 13
\]

Now simplify:

\[
-5x + (7 - x) = 13
\]
\[
-5x + 7 - x = 13
\]
\[
-6x + 7 = 13
\]

Now, subtract 7 from both sides:

\[
-6x = 6
\]

Dividing by -6 gives:

\[
x = -1
\]

Now, we will substitute \( x = -1 \) back into the equation for \( y \):

\[
y = \frac{7 - (-1)}{2}
\]
\[
y = \frac{7 + 1}{2} = \frac{8}{2} = 4
\]

Thus, the solution to the system of equations is:

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

To verify, we can substitute these values back into the original equations:

For the first equation:
\[
3(-1) + 6(4) = -3 + 24 = 21 \quad \text{(True)}
\]

For the second equation:
\[
-5(-1) + 2(4) = 5 + 8 = 13 \quad \text{(True)}
\]

Both equations are satisfied with \( x = -1 \) and \( y = 4 \). Thus, the solution \( \boxed{(-1, 4)} \) is correct.