The problem asks us to solve the system of two linear equations using the substitution method: $-x + 2y = -10$ (1) $6x - y = 16$ (2)

1. Problem Description

The problem asks us to solve the system of two linear equations using the substitution method:

$-x + 2y = -10$ (1)

$6x - y = 16$ (2)

2. Solution Steps

First, we solve the second equation for $y$:

$6x - y = 16$

$y = 6x - 16$

Next, we substitute this expression for $y$ into the first equation:

$-x + 2(6x - 16) = -10$

$-x + 12x - 32 = -10$

$11x = 22$

$x = 2$

Now, we substitute the value of $x$ back into the equation $y = 6x - 16$ to find $y$:

$y = 6(2) - 16$

$y = 12 - 16$

$y = -4$

Therefore, the solution is $(2, -4)$.

3. Final Answer

The solution is $(2, -4)$.