We are given a system of two linear equations with two variables, $x$ and $y$: $4x + y = 14$ $x + 5y = 13$ 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 $y$:

$4x + y = 14$

$x + 5y = 13$

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 $x$:

$y = 14 - 4x$

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

$x + 5(14 - 4x) = 13$

$x + 70 - 20x = 13$

$-19x = 13 - 70$

$-19x = -57$

$x = \frac{-57}{-19}$

$x = 3$

Now that we have the value of $x$, we can substitute it back into the expression for $y$:

$y = 14 - 4x = 14 - 4(3) = 14 - 12 = 2$

Thus, $y = 2$.

We can check our solution by substituting $x=3$ and $y=2$ into both original equations:

$4(3) + 2 = 12 + 2 = 14$, which is correct.

$3 + 5(2) = 3 + 10 = 13$, which is also correct.

3. Final Answer

$x = 3$

$y = 2$