We are given a system of two linear equations with two variables, $x$ and $y$: $2x - 4y = 10$ $x + 5y = 40$ We need to solve this system to find the values of $x$ and $y$.

1. Problem Description

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

$2x - 4y = 10$

$x + 5y = 40$

We need to solve this system to find the values of $x$ and $y$.

2. Solution Steps

We can use the substitution or elimination method. Let's use the substitution method.

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

$x = 40 - 5y$

Now, substitute this expression for $x$ into the first equation:

$2(40 - 5y) - 4y = 10$

$80 - 10y - 4y = 10$

$80 - 14y = 10$

$-14y = 10 - 80$

$-14y = -70$

$y = \frac{-70}{-14}$

$y = 5$

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

$x = 40 - 5(5)$

$x = 40 - 25$

$x = 15$

Thus, the solution to the system of equations is $x = 15$ and $y = 5$.

3. Final Answer

$x = 15, y = 5$