We are asked to solve two systems of linear equations using the substitution method. The first system is: $2x + y = 5$ $x + 3y = 5$ The second system is: $x + 2y = 8$ $2x + 3y = 14$

1. Problem Description

We are asked to solve two systems of linear equations using the substitution method.

The first system is:

$2x + y = 5$

$x + 3y = 5$

The second system is:

$x + 2y = 8$

$2x + 3y = 14$

2. Solution Steps

First system:

$2x + y = 5$

$x + 3y = 5$

Solve the first equation for $y$:

$y = 5 - 2x$

Substitute this into the second equation:

$x + 3(5 - 2x) = 5$

$x + 15 - 6x = 5$

$-5x = -10$

$x = 2$

Substitute $x = 2$ into $y = 5 - 2x$:

$y = 5 - 2(2) = 5 - 4 = 1$

So, $x = 2$ and $y = 1$.

Second system:

$x + 2y = 8$

$2x + 3y = 14$

Solve the first equation for $x$:

$x = 8 - 2y$

Substitute this into the second equation:

$2(8 - 2y) + 3y = 14$

$16 - 4y + 3y = 14$

$-y = -2$

$y = 2$

Substitute $y = 2$ into $x = 8 - 2y$:

$x = 8 - 2(2) = 8 - 4 = 4$

So, $x = 4$ and $y = 2$.

3. Final Answer

For the first system, the solution is $x = 2$ and $y = 1$.

For the second system, the solution is $x = 4$ and $y = 2$.