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

$x + 2y = 1$

$2x + 3y = 4$

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 to eliminate $x$:

$-2(x + 2y) = -2(1)$

$-2x - 4y = -2$

Now we have the following system:

$-2x - 4y = -2$

$2x + 3y = 4$

Add the two equations together:

$(-2x - 4y) + (2x + 3y) = -2 + 4$

$-y = 2$

$y = -2$

Now, substitute $y = -2$ into the first equation $x + 2y = 1$:

$x + 2(-2) = 1$

$x - 4 = 1$

$x = 1 + 4$

$x = 5$

So the solution is $x = 5$ and $y = -2$.

3. Final Answer

The solution is $x = 5$ and $y = -2$.