Question

Solve the system of equations.
7x+3y=−25
−7x+9y=−47
(1 poi

Answer 1

To solve the system of equations

\[
7x + 3y = -25 \quad (1)
\]
\[
-7x + 9y = -47 \quad (2)
\]

we can use the method of elimination. First, we can add equations (1) and (2) to eliminate \( x \).

Adding the two equations:

\[
(7x - 7x) + (3y + 9y) = -25 - 47
\]

This simplifies to:

\[
0 + 12y = -72
\]

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

\[
12y = -72
\]
\[
y = -6
\]

Now that we have \( y \), we can substitute \( y = -6 \) back into equation (1) to find \( x \):

\[
7x + 3(-6) = -25
\]

This simplifies to:

\[
7x - 18 = -25
\]

Now, add 18 to both sides:

\[
7x = -25 + 18
\]
\[
7x = -7
\]

Now, divide by 7:

\[
x = -1
\]

The solution to the system of equations is:

\[
x = -1, \quad y = -6
\]

So the solution is:

\[
\boxed{(-1, -6)}
\]