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 find the values of $x$ and $y$ that satisfy both equations.

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 find the values of $x$ and $y$ that satisfy both equations.

2. Solution Steps

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

Multiply the first equation by 2:

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

$12x - 2y = 36$

Now we have the following system of equations:

$12x - 2y = 36$

$4x + 2y = 26$

Add the two equations together:

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

$16x = 62$

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

Substitute the value of $x$ into the first original equation:

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

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

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

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

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

3. Final Answer

The solution to the system of equations is $x = \frac{31}{8}$ and $y = \frac{21}{4}$.

Final Answer: $x = \frac{31}{8}, y = \frac{21}{4}$