Solve the following system of linear equations: $6x - 3y = 39$ $-3x - 8y = 39$

1. Problem Description

Solve the following system of linear equations:

$6x - 3y = 39$

$-3x - 8y = 39$

2. Solution Steps

We can use the substitution or elimination method to solve this system. Let's use the elimination method. Multiply the second equation by 2 to eliminate $x$.

$2(-3x - 8y) = 2(39)$

$-6x - 16y = 78$

Now add the modified second equation to the first equation:

$(6x - 3y) + (-6x - 16y) = 39 + 78$

$6x - 3y - 6x - 16y = 117$

$-19y = 117$

Solve for $y$:

$y = \frac{117}{-19}$

$y = -\frac{117}{19}$

Now substitute the value of $y$ into the first equation $6x - 3y = 39$:

$6x - 3(-\frac{117}{19}) = 39$

$6x + \frac{351}{19} = 39$

$6x = 39 - \frac{351}{19}$

$6x = \frac{39 \cdot 19}{19} - \frac{351}{19}$

$6x = \frac{741}{19} - \frac{351}{19}$

$6x = \frac{390}{19}$

$x = \frac{390}{19 \cdot 6}$

$x = \frac{390}{114}$

$x = \frac{65}{19}$

3. Final Answer

$x = \frac{65}{19}$

$y = -\frac{117}{19}$