Question

Find the solution of the system of equations.
x, minus, 6, y, equals, minus, 35
x−6y=
−35
minus, 7, x, minus, 6, y, equals, minus, 43
−7x−6y=
−43

Answer 1

To solve the system of equations:

1. \( x - 6y = -35 \) (Equation 1)
2. \( -7x - 6y = -43 \) (Equation 2)

We'll use the substitution or elimination method. Let's start with substitution.

From Equation 1, we can solve for \( x \):

\[
x = 6y - 35
\]

Now, substitute \( x \) into Equation 2:

\[
-7(6y - 35) - 6y = -43
\]

Distributing the \(-7\):

\[
-42y + 245 - 6y = -43
\]

Combine like terms:

\[
-48y + 245 = -43
\]

Now, isolate \( y \):

\[
-48y = -43 - 245
\]
\[
-48y = -288
\]
\[
y = \frac{-288}{-48}
\]
\[
y = 6
\]

Now substitute \( y = 6 \) back into Equation 1 to find \( x \):

\[
x - 6(6) = -35
\]
\[
x - 36 = -35
\]
\[
x = -35 + 36
\]
\[
x = 1
\]

The solution to the system of equations is:

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