The problem is to solve the system of linear equations: $4x + y = 6$ $3x - y = 8$

1. Problem Description

The problem is to solve the system of linear equations:

$4x + y = 6$

$3x - y = 8$

2. Solution Steps

We can solve this system of equations using elimination.

Add the two equations together:

$(4x + y) + (3x - y) = 6 + 8$

$7x = 14$

Divide both sides by 7:

$x = \frac{14}{7}$

$x = 2$

Now, substitute the value of $x$ into either of the original equations to solve for $y$.

Let's use the first equation:

$4x + y = 6$

$4(2) + y = 6$

$8 + y = 6$

Subtract 8 from both sides:

$y = 6 - 8$

$y = -2$

3. Final Answer

The solution to the system of equations is $x = 2$ and $y = -2$.

So the solution is $(2, -2)$.