We are given a system of two linear equations with two variables, $x$ and $y$: $x + 2y = 17$ $8x + 3y = 45$ We need to solve for $x$ and $y$.

1. Problem Description

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

$x + 2y = 17$

$8x + 3y = 45$

We need to solve for $x$ and $y$.

2. Solution Steps

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

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

$x = 17 - 2y$

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

$8(17 - 2y) + 3y = 45$

Expand and simplify the equation:

$136 - 16y + 3y = 45$

$136 - 13y = 45$

$-13y = 45 - 136$

$-13y = -91$

$y = \frac{-91}{-13}$

$y = 7$

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

$x = 17 - 2(7)$

$x = 17 - 14$

$x = 3$

So the solution is $x=3$ and $y=7$.

3. Final Answer

$x = 3$ and $y = 7$