Question

find the solution of the system of equations.\

$$\begin{cases}-x - y = -1\\\\-x + 5y = 11\\end{cases}$$

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} -x - y = -1 \\ -x + 5y = 11 \end{cases}$$

Subtract the first equation from the second equation:
$$(-x + 5y) - (-x - y) = 11 - (-1)$$
Simplify the left side: $-x + 5y + x + y = 6y$
Simplify the right side: $11 + 1 = 12$
So we get $6y = 12$.

Step2: Solve for y

Divide both sides of $6y = 12$ by 6:
$$y = \frac{12}{6} = 2$$

Step3: Substitute y into first equation

Substitute $y = 2$ into $-x - y = -1$:
$$-x - 2 = -1$$
Add 2 to both sides:
$$-x = -1 + 2 = 1$$
Multiply both sides by -1:
$$x = -1$$

Answer:

$x = -1$, $y = 2$