Question

Solve the system of equations.
7x+3y=−25

−7x+9y=−47

Answer 1

To solve the system of equations:

1. \( 7x + 3y = -25 \) (Equation 1)
2. \( -7x + 9y = -47 \) (Equation 2)

We can use either the substitution method or the elimination method. Here, we'll use the elimination method.

First, we can add Equation 1 and Equation 2 together to eliminate \( x \):

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

This simplifies to:

\[
0 + 12y = -72
\]

Now we can solve for \( y \):

\[
12y = -72
\]
\[
y = \frac{-72}{12} = -6
\]

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

\[
7x + 3(-6) = -25
\]
\[
7x - 18 = -25
\]
\[
7x = -25 + 18
\]
\[
7x = -7
\]
\[
x = \frac{-7}{7} = -1
\]

So, the solution to the system of equations is:

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

Thus, the solution is \( (x, y) = (-1, -6) \).