We need to solve four linear equations for the unknowns $w$, $k$, $t$, and $r$. The equations are: 1. $\frac{w}{-8} - 5 = -6$

1. Problem Description

We need to solve four linear equations for the unknowns $w$, $k$, $t$, and $r$. The equations are:

1. $\frac{w}{-8} - 5 = -6$

2. $17 = -5k + 2$

3. $\frac{t}{3} + 4 = 10$

4. $-5 = 7 + 3r$

2. Solution Steps

Equation 1: $\frac{w}{-8} - 5 = -6$

* Add 5 to both sides:

$\frac{w}{-8} - 5 + 5 = -6 + 5$

$\frac{w}{-8} = -1$

* Multiply both sides by -8:

$\frac{w}{-8} \times (-8) = -1 \times (-8)$

$w = 8$

Equation 2: $17 = -5k + 2$

* Subtract 2 from both sides:

$17 - 2 = -5k + 2 - 2$

$15 = -5k$

* Divide both sides by -5:

$\frac{15}{-5} = \frac{-5k}{-5}$

$-3 = k$

$k = -3$

Equation 3: $\frac{t}{3} + 4 = 10$

* Subtract 4 from both sides:

$\frac{t}{3} + 4 - 4 = 10 - 4$

$\frac{t}{3} = 6$

* Multiply both sides by 3:

$\frac{t}{3} \times 3 = 6 \times 3$

$t = 18$

Equation 4: $-5 = 7 + 3r$

* Subtract 7 from both sides:

$-5 - 7 = 7 + 3r - 7$

$-12 = 3r$

* Divide both sides by 3:

$\frac{-12}{3} = \frac{3r}{3}$

$-4 = r$

$r = -4$

3. Final Answer

$w = 8$

$k = -3$

$t = 18$

$r = -4$