Question

y = -2x - 2 and 2x - 2y = 5

Answer 1

To solve the system of equations given by:

1. \( y = -2x - 2 \) (Equation 1)
2. \( 2x - 2y = 5 \) (Equation 2)

we can substitute Equation 1 into Equation 2 to eliminate \( y \).

Substituting \( y \) from Equation 1 into Equation 2:

\[
2x - 2(-2x - 2) = 5
\]

Now simplify it:

\[
2x + 4x + 4 = 5
\]

Combine like terms:

\[
6x + 4 = 5
\]

Next, subtract 4 from both sides:

\[
6x = 1
\]

Now, divide by 6:

\[
x = \frac{1}{6}
\]

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

\[
y = -2\left(\frac{1}{6}\right) - 2
\]

Calculating it gives us:

\[
y = -\frac{2}{6} - 2 = -\frac{1}{3} - 2 = -\frac{1}{3} - \frac{6}{3} = -\frac{7}{3}
\]

So, the solution to the system of equations is:

\[
\left( x, y \right) = \left( \frac{1}{6}, -\frac{7}{3} \right)
\]