The problem is to solve the following system of equations: $7x = -3 + 10y$ $9 - 3x = 6y$

1. Problem Description

The problem is to solve the following system of equations:

$7x = -3 + 10y$

$9 - 3x = 6y$

2. Solution Steps

First, we can isolate $x$ in the second equation:

$9 - 3x = 6y$

$9 - 6y = 3x$

$3x = 9 - 6y$

$x = (9 - 6y) / 3$

$x = 3 - 2y$

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

$7x = -3 + 10y$

$7(3 - 2y) = -3 + 10y$

$21 - 14y = -3 + 10y$

$21 + 3 = 10y + 14y$

$24 = 24y$

$y = 1$

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

$x = 3 - 2y$

$x = 3 - 2(1)$

$x = 3 - 2$

$x = 1$

Therefore, the solution to the system of equations is $x = 1$ and $y = 1$.

3. Final Answer

$x = 1$

$y = 1$