Find the solution of the system of equations.

Question

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:

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