We are given a system of two linear equations with two variables, $x$ and $y$. The system is: $6x - y = 18$ $4x + 2y = 26$ We need to solve for $x$ and $y$.

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$. The system is:

$6x - y = 18$

$4x + 2y = 26$

We need to solve for $x$ and $y$.

2. Solution Steps

We can use the substitution or elimination method to solve this system. Let's use the elimination method.

First, multiply the first equation by 2:

$2(6x - y) = 2(18)$

$12x - 2y = 36$

Now we have the following system:

$12x - 2y = 36$

$4x + 2y = 26$

Add the two equations together to eliminate $y$:

$(12x - 2y) + (4x + 2y) = 36 + 26$

$16x = 62$

Now, solve for $x$:

$x = \frac{62}{16} = \frac{31}{8}$

Now that we have the value of $x$, substitute it into one of the original equations to solve for $y$. Let's use the first equation:

$6x - y = 18$

$6(\frac{31}{8}) - y = 18$

$\frac{186}{8} - y = 18$

$\frac{93}{4} - y = 18$

$y = \frac{93}{4} - 18$

$y = \frac{93}{4} - \frac{72}{4}$

$y = \frac{21}{4}$

3. Final Answer

$x = \frac{31}{8}$

$y = \frac{21}{4}$

Final Answer: $x = 31/8, y = 21/4$