The problem is to solve the system of two linear equations with two variables: $x + y = 9$ $2x + 3y = 17$

1. Problem Description

The problem is to solve the system of two linear equations with two variables:

$x + y = 9$

$2x + 3y = 17$

2. Solution Steps

We will use the substitution or elimination method to solve this system of equations. Let's use the substitution method.

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

$x = 9 - y$

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

$2(9 - y) + 3y = 17$

$18 - 2y + 3y = 17$

$18 + y = 17$

$y = 17 - 18$

$y = -1$

Now, substitute the value of $y$ back into the expression for $x$:

$x = 9 - (-1)$

$x = 9 + 1$

$x = 10$

So, the solution is $x = 10$ and $y = -1$.

Let's check the solution in both original equations:

Equation 1: $x + y = 9$

$10 + (-1) = 9$

$9 = 9$ (True)

Equation 2: $2x + 3y = 17$

$2(10) + 3(-1) = 17$

$20 - 3 = 17$

$17 = 17$ (True)

3. Final Answer

$x = 10$

$y = -1$