We are given a system of two linear equations with two variables, $x$ and $y$: $4x + y = 1$ $2x + 3y = 8$ 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 $y$:

$4x + y = 1$

$2x + 3y = 8$

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

2. Solution Steps

We can solve this system of equations using the substitution or elimination method. Let's use the substitution method.

From the first equation, we can express $y$ in terms of $x$:

$y = 1 - 4x$

Now substitute this expression for $y$ into the second equation:

$2x + 3(1 - 4x) = 8$

Expand and simplify the equation:

$2x + 3 - 12x = 8$

$-10x + 3 = 8$

$-10x = 8 - 3$

$-10x = 5$

$x = \frac{5}{-10}$

$x = -\frac{1}{2}$

Now substitute the value of $x$ back into the equation $y = 1 - 4x$:

$y = 1 - 4(-\frac{1}{2})$

$y = 1 + 2$

$y = 3$

So the solution is $x = -\frac{1}{2}$ and $y = 3$.

3. Final Answer

$x = -\frac{1}{2}, y = 3$